If a Christian woman becomes Muslim and she is the wife of a Christian man, the marriage contract is annulled.  Based on that, it is not permissible for her to stay with him even if they are old and have no sexual relationship. End quote. 

Fataawa al-Lajnah al-Daa’imah, 19/16-17 

It does not make it permissible to you to stay in the same house as a non-Muslim man. Think positively of Allah, may He be exalted, for He is the One Who says (interpretation of the meaning):

“Allaah will grant after hardship, ease”

[al-Talaaq 65:7]. 

With that being said. You have to remember that your aim is to please Allah (swt) before pleasing the people around you. Even if you would argue that the kids will loose their parents being together but you should remember that Allah (swt) He would gave you and your children life could make their lives much better than in your current situation.

I would end up this by saying that you should sit down with your husband and explain him calmly that there is no way for this to continue. Allah knows best but maybe he would re-consider Islam (not because of you but rather because of the meaning of why Allah (swt) has forbade us to be around non-Muslims when it could harm our faith). He seems to be understanding of your conversion but he also needs to understand that it is unlawful for him to be with you.