What is the ruling regarding my remaining married to a non-Muslim woman who has no interest in Islam, given my desire to stay away from the unlawful (haram) and to raise my children upon Islam?

Allah has forbidden marriage to idolatrous women, with the exception of the People of the Book, due to His Almighty saying: "And do not marry polytheistic women until they believe." The women of the People of the Book were exempted in His Almighty saying: "and the chaste women from among those who were given the Scripture before you," because they are closer to Muslims in some beliefs.

Marriage to a woman from the People of the Book is only permissible under two conditions: that she is chaste, and that she is actually Christian or Jewish.

If the wife does not believe in any religion, the marriage is invalid and must be annulled immediately, according to His Almighty saying: "and do not hold on to the marriage bonds of disbelieving women." As for the children, they are attributed to the father, and the invalidity of the marriage does not affect this attribution, in order to preserve the child's right and the Lawgiver's eagerness to establish lineage. As Ibn Taymiyyah said: "Indeed, Muslims are in agreement that every marriage that the husband believed to be permissible, if he engaged in intercourse within it, then his child is attributed to him and they inherit from each other by the consensus of Muslims, even if that marriage was invalid in reality by the consensus of Muslims."