As Andrea said, it doesn't look good. If you mean with "illegal" that he crossed the border without any inspection or papers to come to the US, you could not even have "fixed" his status easily without him having a criminal record.
The fact that he now also has a felony record, makes things even worse.
If you want to do anything, you definitely need to consult an attorney about the few options you might have.
Wolf W. Kaufmann
Southern California Immigration Attorney
This post is intended to be of general educational nature only and cannot be a substitute for detailed legal advice in your case. No attorney-client relationship is being created by this post.
Because your husband apparently entered the US illegally, and because he now has a family violence charge and a felony, it is very unlikely that he will be given a green card. In fact, I am very surprised that he has not been processed for removal during one of his prior arrests. Good Luck