Marriage between a non-Muslim man and a Muslim woman is forbidden and invalid. It is absolutely not permissible under any circumstance in Islamic law (shari’a) of Allah, for a non-Muslim man to marry a Muslim woman, as Allah says in the Quran:
“And give not (your daughters) in marriage to disbelievers until they believe.” (2:221)
Allah also says: “They (Muslim women) are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them.” (60:10)
If a Muslim woman marries a kaafir (disbeliever), then she is a zaaniyah (adulteress), the children are the children of zina (fornication) and her punishment is the punishment for adultery. If she was ignorant of the ruling then she is excused, but they must be separated, and there is no need for a divorce because the marriage is null and void.