Muslim Man and Non-Muslim WomanIn general, Muslim men are not permitted to marry non-Muslim women. "Do not marry unbelieving women until they believe. A slave woman who believes is better than an unbelieving woman, even though she allures you.... Unbelievers beckon you to the Fire. But Allah beckons by His Grace to the garden of bliss and forgiveness. And He makes His signs clear to mankind, that they may receive admonition" (Qur'an 2:221).
An exception is made for Muslim men to marry chaste or pious Jewish and Christian women, who are referred to as "People of the Book." This comes from the understanding that Jews and Christians share similar religious outlooks - a belief in One God, following the commandments of Allah, a belief in revealed scripture (Books), etc. "This day are all things good and pure made lawful to you.... Lawful to you in marriage are not only chaste women who are believers, but chaste women among the People of the Book, revealed before your time, when you give them their due dowers, and desire chastity not lewdness. If any one rejects faith, fruitless is his work, and in the Hereafter he will be in the ranks of those who have lost" (Qur'an 5:5).
The children of such a union are always to be raised in the faith of Islam. This should be discussed thoroughly by the couple before they decide to marry.