@karen12344,
You repeatedly wrote what he has done in the past, DUI's, drug use, heavy drinking, assault charge, etc., but you fail to mention or state that he has cleaned up his act and does not drink, etc. (You did write that he used to do drugs, which I guess indicates that he does not do so anymore.) So, has he quit the drinking? Does he still keep drugs around for use or for selling?
I believe people can indeed change, at least to some degree. You need to keep some distance and let him prove to you that he has changed. Not just for a month or two, but maybe for up to a year. In other words, he must prove he has changed before you get involved. Do not get involved believing you will help change him. It very rarely works that way. And don't, I repeat, don't put yourself in a position where you might get pregnant by this guy. And yes, that may well mean no sex. Even the best birth control fails. You need to be absolutely certain he has changed. Otherwise, you are only asking for trouble.
Bottom line, I won't tell you to stay away, but PLEASE be careful. Hopefully he has changed. You say he is going to church, and I have seen miraculous changes in people who turn to God to help overcome issues in life. So that is a plus for him. And the fact that he has a child should provide him motivation to get his life together and stop the destructive behavior. But you need to be certain before getting too involved.
Good luck to you. Be smart. It is better to walk away now if you have any doubts at all about his changes.