According to traditional schools of Islamic law, a marriage between a Muslim and a non-Muslim is null; they should immediately separate. The following verse is their profound evidence on this issue:
“Do not marry mushrik women (who interpose others between herselves and God) until they trust only in God. A captive woman who trusts only in God is better than a mushrik woman even if she (the mushrik) has impressed you much. Do not wed your women to mushrik men (who interpose others between himselves and God) until they trust only in God. A captive man who trusts only in God is better than a mushrik man even if he (the mushrik) has impressed you much.” (Al-Baqarah/The Cow 2:221)
The 10th verse of Surah Al-Mumtahinah is also claimed to provide evidence on this topic. It will be explained later, that it cannot.
The following verse permits men to marry women of Ahl al-Kitab (People of the Book):
وَالْمُحْصَنَاتُ مِنَ الَّذِينَ أُوتُواْ الْكِتَابَ مِن قَبْلِكُمْ إِذَا آتَيْتُمُوهُنَّ أُجُورَهُنَّ مُحْصِنِينَ غَيْرَ مُسَافِحِينَ وَلاَ مُتَّخِذِي أَخْدَانٍ
“And lawful in marriage are chaste women from among the believers and chaste women from among those who were given the Book before you, when you give their mehr, desire chastity, not take secret lovers.” (Al-Ma’ida/ The Feast 5:5)
The following verse makes clear that the Ahl al-Kitab are mushrik:
اتَّخَذُواْ أَحْبَارَهُمْ وَرُهْبَانَهُمْ أَرْبَابًا مِّن دُونِ اللّهِ وَالْمَسِيحَ ابْنَ مَرْيَمَ وَمَا أُمِرُواْ إِلاَّ لِيَعْبُدُواْ إِلَـهًا وَاحِدًا لاَّ إِلَـهَ إِلاَّ هُوَ سُبْحَانَهُ عَمَّا يُشْرِكُونَ
“They have taken their scholars and clergies as lords before Allah, and also the Messiah, the son of Mary. Although, they were commanded only to worship one God. There is no deity except Him. Exalted is Allah above whatever they associate with Him.” (At-Tawbah/ The Repentance 9:31)
Consent to marry the People of Book is a consent to marry the mushrik. Yet, the following command is for men in the foregoing verse:
“Do not marry mushrik women (who interpose others between herselves and God) until they trust only in God. A captive woman who trusts only in God is better than a mushrik woman even if she (the mushrik) has impressed you much.” (Al-Baqara/ The Cow 2:221)
The phrases ‘a captive man who trusts only in God is better than a mushrik man‘ and ‘a captive woman who trusts only in God is better than a mushrik woman’ do not designate that such a marriage is forbidden because, the word “better” is used when comparing two “goods”. Therefore, this verse can NOT be interpreted as a prohibition for believing women to marry mushrik men, and believing men to marry mushrik women. The practice of our Prophet is also in this direction:
Abu-l As bin ar-Rabi was the son in law of our Prophet (p.b.u.h). He married Zaynab before Islam, yet he did not convert into Islam. When he was captured in the battle of Badr, Zaynab had sent the necklace, which her mother gave when they married, together with some amount of property, as a ransom. Feeling sorry about the situation, the Prophet (p.b.u.h) asked to return the necklace to Zaynab and immediately release Abu’l As. He requested from Abu’l As to send his daughter to Medina. He, though felt a great love for his wife, kept his promise, and sent Zaynab to Medina.
When, in 6th century after hijra, Abu’l As was returning from Syria together with the commercial goods the mushriks entrusted to him, the caravan was captured by Muslim, but he escaped. Zaynab took him under her patronage as he went to her at night. Our Prophet said to the warriors that the war loots were theirs, but that he would be please if they returned them to Abu’l As. Thereupon, all of the goods in the caravan were returned to Abu’l As.
Upon his arrival at Makkah, Abu’l As delivered the trusts to their owners and converted into Islam, and migrated to Medina . Our Prophet returned Zaynap, after a period of six years, to him under their formed marriage . Because the fact that Abu’l As was a concealer (kafir) did not invalidate his marriage with Zaynab.
As narrated by Ibn Shihab, “In the time of the Messenger of Allah (p.b.u.h), some women converted into Islam in their homelands, yet they did not migrate . While they became Muslims, their husbands remained as concealers. The daughter of Walid Ibn al-Mughira was among these. She was married with Safwan Ibn Umayya; she became Muslim on the day of Conquest (of Makkah), yet her husband Safwan escaped from Islam. As a sign of confidence, the Messenger of Allah gave him his own robe and sent him after Wahb Ibn Umayr, son of his uncle. He was calling him to Islam and to come to him; he would accept it if he liked, otherwise he would travel without any restriction for two months. When Safwan came to the Messenger of Allah with the robe, he said, with a loud voice amidst the public:
“O Muhammad ! “Wahb Ibn Umayr brought me your robe; he said you called me to you, that I may accept if I like it, otherwise I am granted with two months.”
The Messenger of Allah said: “Abu Wahb, come down!”, but he said : “No, by God, I shall not come down unless you explain to me!”. Upon this he said: “No, you can travel freely for four months.” Sawfan’s wife was a Muslim. Our Prophet did not let Safwan and his wife separate until he became a Muslim. His wife remained with him with their former marriage bond .
The first event took place before the treaty of Hudaybiya, while the second was after the conquest of Makkah. The scholars claim that the phrase “They are not lawful for the disbelievers, nor are the disbelievers lawful for them” in verse 10 of Surat al-Mumtahinah is an evidence that it is unlawful for a Muslim woman to marry a non-Muslim. This verse, which is revealed before both events we have explained, provides for the situation after the justification asserted by a woman, whom the husband had decided to divorce, is found to be rightful by the adjudicator or court. This issue will be dealt with below. Our Prophet (p.b.u.h) had not separated any wife and husband due to the difference of religions. If what is said had been true, this would absolutely have a practical example.
Women who are prohibited to be married are listed from verses 22 to 24 of Surat an-Nisa, which does not include any account on diversity of religions. It is required in verse 25 that those who do not have the power to marry chaste Muslim women should marry chaste Muslim captive, but recommended to endure instead of marrying them. Accordingly, the first preference is on chaste Muslim women, followed by chaste Muslim captive. Since marriage with chaste women of Ahl al-Kitab is permitted in verse 5 of Surat al-Maida, it follows that they are the third preference in marriage. Therefore, a chaste Muslim captive is better than a chaste Ahl al-Kitab woman. As marriage with a chaste Muslim captive is not recommended, marriage with a chaste Ahl al-Kitab woman is not recommended at all, but is not prohibited. Ahl al-Kitab are also mushrik. For that reason, the verse mentions marriage with mushrik disregarding any account on the difference between sexes.
“Do not marry mushrik women (who interpose others between herselves and God) until they trust only in God. A captive woman who trusts only in God is better than a mushrik woman even if she (the mushrik) has impressed you much. Do not wed your women to mushrik men (who interpose others between himselves and God) until they trust only in God. A captive man who trusts only in God is better than a mushrik man even if he (the mushrik) has impressed you much. They invite you to the Fire but God invites you, by His leave, to the Gardens and to forgiveness. He manifests His verses to the people so that they may come to their senses.” (Al-Baqarah/ The Cow 2:221)
The absolute must in verses is chastity. For that reason, an adulterer Muslim may only marry an adulteress Muslim, or a mushrik. Allah (SWT) commands:
الزَّانِي لَا يَنْكِحُ إِلَّا زَانِيَةً أَوْ مُشْرِكَةً وَالزَّانِيَةُ لَا يَنْكِحُهَا إِلَّا زَانٍ أَوْ مُشْرِكٌ وَحُرِّمَ ذٰلِكَ عَلَى الْمُؤْمِنِينَ.
“A man guilty of adultery shall not marry any but the woman guilty of the same or a mushrik woman, and none shall marry a woman guilty of adultery but the man guilty of the same or a mushrik man. Such marriages are forbidden to true believers.” (An-Noor / The Light 24:3)
“There was a man named Marsad Ibn Abu Marsad. He used to take the prisoners of war from Makkah, and travel them to Medina. He had a prostitute friend named Anak. He had promised one of the Makkan prisoners to carry him off.
Marsad says: At a moonlit night, I arrived at the shadow of one of the walls of Makkah. Just at that moment Anak came, she saw my shadow at the base of wall. She recognized me as she came nearby, and said “Is that Marsad?”. “Yes, Marsad”, I said. “Hello, and welcome. Come and stay with us for the night!”. Once I said “No, Anak, Allah prohibited adultery”, she began to scream. “Hey, the inhabitants of tents! This man is taking your prisoners away!”, she said. Instantly eight persons gave chase to me. I turned to Handeme road, entered to a cave or a pit. The followers came, stood by me, and peed. Their urine touched my head. But Allah kept me away from their sight. Then they went away. I loaded my friend, who was a fat one, on my back. I arrived at Izhir, unfastened his handcuffs. I started to carry him on my back again , which exhausted me. Eventually I arrived at Medina. I appeared before the Messenger of Allah (p.b.u.h): I said “Oh the Messenger of Allah! I will marry Anak.” He remained silent, and not responded until the following verse was revealed:
“The adulterer shall not marry save an adulteress or a mushrik, and the adulteress none shall marry save an adulterer or a mushrik..” (An-Noor / The Light 24:3)
Then he said : “See Marsad, an adulterer may only marry an adulteress or a mushrik woman, An adulteress may only marry an adulterer or a mushrik man. Do not marry her!” 
Our Prophet justified his order “Do not marry her!” not because of her belief , but because of her adultery. As a matter of fact, it is hard to understand the schools of law although the situation is so clear. It is claimed that this verse is abrogated with the verse “Marry those among you who are single…” (An-Noor / The Light 24:32)
Ibn Hazm says that this claim has no grounds. It is not possible to say that a verse or a saying of the Prophet is “abrogated (mansukh)” unless there is an accurate evidence.
These words of Ibn Hazm are true, however, he also says that only an adulterer may marry the chaste women of Ahl al-Kitab, though the verse explicitly declares that the adulterer or adulteress shall marry a mushrik . It is hard to understand Ibn Hazm in terms of the basis on which he relies to restrict this with Ahl al-Kitab, and also he does not accept that an adulteress Muslim may marry a mushrik man.