The Quran lays out clear guidelines for marriage. One of the main traits Muslims should look for in a potential spouse is a similarity in religious outlook. For the sake of compatibility and the upbringing of future children, Islam recommends that a Muslim marry another Muslim. However, in some circumstances, it is permissible for a Muslim to marry a non-Muslim. The rules in Islam regarding interfaith marriage are based on protecting the religion and deterring both man and woman from doing things that jeopardize their faith.
Muslim Man and Non-Muslim Woman
In 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 of interfaith marriage in Islam is made for Muslim men to marry pious Jewish and Christian women or women who don't engage in immoral conduct (chaste women). This is because marriage is not based on fulfilling sexual desires. Instead, it is an institution that establishes a home built on tranquility, faith, and Islamic morals. The exception 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, 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 anyone rejects faith, fruitless is his work, and in the Hereafter, he will be in the ranks of those who have lost." (Quran 5:5).
The children of such a union are always to be raised in the faith of Islam. The couple should thoroughly discuss child rearing before they decide to marry.
Muslim Woman and Non-Muslim Man
Interfaith marriage for an Islamic woman is taboo in Islam, and Muslim women are formally forbidden from doing so—except in Tunisia, which has made it legal for Muslim women to marry non-Muslim men. The same verse cited above (2:221) says:
"Nor marry your girls to unbelievers until they believe. A man slave who believes is better than an unbeliever." (Quran 2:221)
In every country other than Tunisia, no exception is given for women to marry Jews and Christians—even if they convert—so the law stands that she may only marry a believing Muslim man. As head of the household, the husband provides leadership for the family. A Muslim woman does not follow the leadership of someone who does not share her faith and values.