All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The marriage of your husband to this non-Muslim woman if she is not from the people of the book is invalid as it is not permissible for a Muslim man to marry a non-Muslim woman unless she is from the people of the book. Allaah says (which means): {And do not marry Al-Mushrikaat (idolatresses, etc.) till they believe (worship Allaah Alone).}[2:221]. However, if this woman is from the People of the Book and the marriage met the correct marriage requirements, the most important of which is the presence of the guardian and the witnesses, then his marriage to her is correct if it took place after repentance and after making sure that the womb did not conceive from the abominable sin of adultery. However, if the marriage took place before repentance and before making sure that she did not become pregnant from fornication, the scholars differed about the ruling on such marriage. Nonetheless, some scholars consider it to be correct.
Moreover, it should be noted that if your husband fears a harm by being married to this woman, it is more appropriate for him to divorce her, as it is very rare for a marriage with a woman of the people of the book to be free from disadvantages and harms; this is in relation to your husband.
As far as you are concerned, we advise you to be patient with him and you should advise him in good words about his mistakes and warn him about things that could have a bad effect on the education of the children. Concerning your rights on him, he has to be just with you with regard to providing for you and spending the night with you. If he meets these requirements, then it does not matter whether he continues his marriage to this woman or divorces her. Finally, you should bring up your children according to Islamic creed and morals.
Allaah knows best.