With regard to marrying a Christian or Jewish woman, this is permissible according to the text of the Qur’aan. Allaah says (interpretation of the meaning):
“Made lawful to you this day are At‑Tayyibaat [all kinds of Halaal (lawful) foods, which Allaah has made lawful (meat of slaughtered eatable animals, milk products, fats, vegetables and fruits)]. The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due Mahr (bridal-money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as girlfriends”
[al-Maa’idah 5:5]
Ibn al-Qayyim said:
It is permissible to marry a woman from the People of the Book. Allaah says (interpretation of the meaning):
“(Lawful to you in marriage) are chaste [muhsan] women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time”
[al-Maa’idah 5:5]
Muhsan here means chaste; the same word is also used in Soorat al-Nisa’ to describe married women, who are forbidden in marriage to anyone else. And it was said that the chaste women to whom marriage is permitted is free women, so slave women from the People of the Book are not permissible. However, the first view is the one which is correct, for several reasons…
The point is that Allaah has permitted us to marry chaste women from among the People of the Book, and the companions of the Prophet (peace and blessings of Allaah be upon him) did that. ‘Uthmaan married a Christian woman, as did Talhah ibn ‘Ubayd-Allaah; and Hudhayfah married a Jewish woman.
‘Abd-Allaah ibn Ahmad said: I asked my father about a Muslim man who married a Christian or Jewish woman. He said: I do not like for him to do it, but if he does, then some of the companions of the Prophet (peace and blessings of Allaah be upon him) did that too.
Ahkaam Ahl al-Dhimmah, 2/794, 795.