It is haram for a Muslim woman to marry a non-Muslim man, regardless of whether he is of the People of the Book or not. Allah Almighty says in Quran,
"...And do not marry (your girls) to idolaters until they believe...." (Surah 2: Verse 221)
And He said concerning the immigrant Muslim women,
"...Then if you know them to be Believers, do not send them back to the unbelievers. They are not halal for them (as wives), nor are they halal for them (as husbands)." (Surah 60: Verse 10)
No text exists which makes exceptions for the People of the Book, hence, on the basis of the above verses, there is a consensus among Muslims concerning this prohibition. Thus, while a Muslim man is permitted to marry a Christian or Jewish woman, a Muslim woman is not allowed to marry a Christian or Jewish man.
There are many sound reasons for this difference. First, the man is the head of the household, the one who maintains the family, and he is responsible for his wife. And while Islam guarantees freedom of belief and practice to the Christian or Jewish wife of a Muslim, safeguarding her rights according to her own faith, other religions, such as Judaism and Christianity, do not guarantee the wife of a different faith freedom of belief and practice, nor do they safeguard her rights.
Since this is the case, how can Islam take chances on the future of its daughters by giving them into the hands of people who neither honor their religion nor are concerned to protect their rights? A marriage between a man and woman of different faiths can be based only on the husband’s respect for his wife’s beliefs; otherwise a good relationship can never develop.
Now, the Muslim believes that both Judaism and Christianity originated in divine revelation, although later distortions were introduced into them. He also believes that God revealed the Taurat to Moses and the Injeel to Jesus, (Taurat refers to the original scripture revealed to the Prophet Moses by God, and Injeel to the Prophet Isa (Jesus). These are not to be confused with either the existing Torah or Old Testament, or the four Gospels of the New Testament.
Accordingly, the Christian or Jewish wife of a Muslim lives under the protection of a man who respects the basic tenets of her faith, her scripture, and her prophets, while in contrast to this the Jew or Christian recognizes neither the divine origin of Islam, its Book, or its Prophet (peace be on him). How then could a Muslim woman live with such a man, while her religion requires of her the observance of certain worships, duties, and obligations, as well as certain prohibitions.
It would be impossible for the Muslim woman to retain her respect for her beliefs as well as to practice her religion properly if she were opposed in this regard by the master of the house at every step. It will be realized from this that Islam is consistent with itself in prohibiting the Muslim man to marry a mushrik woman, for since Islam is absolutely opposed to shirk, it would obviously be impossible for two such people to live together in harmony and love.