If he's reading up on it and pushing himself as much as he can to get better, it will get better for the both of you. I know every survivor has a different level of ability and willingness to work on this, but if he's really trying to push forward, things should get better in time.
I don't know what he saw modeled by his parents as far as being a loving couple goes, but in my case I've had to reinvent what that means from scratch. My earliest memories of my Dad were of how "fat and ugly" (his words) my Mom was, how cute the woman at the bank down the street was, etc. While they kissed once in a while in front of us kids, I knew from my earliest days what a sham it was.
The point is, I grew up without a clue about what being in a happy relationship looked like, and your husband might be in the same boat. I know this sounds like it should be self-evident, especially if your parents were happy and showed it, but believe me, it can be harder than it should be for some.
I love my wife to death, but I have to go out of my way to show her that frequently (and sometimes I don't do it nearly as well as I should.) For me, this means making time, being there even if I'm tired, etc., being involved in things that matter to her, and so on. While most guys would do these things automatically, anyone who's watched his parents hate each other for however many years might be on a learning curve. All I can say is that my heart is with you and I hope things get better soon.
Never worry about "three steps forward and two steps back." Thirty steps forward and twenty back are still ten steps in the right direction.