Hello, and welcome! This is a great board, and you will find a lot of wisdom, advice and compassion here. I am very sorry for the situation that brings you here, but I'm glad you are here.
Everyone is different in their motivation to get sober, and some people never do. In my case, I decided not to live with the drinking, and I left my AH in October. However, my leaving wasn't about him. It was about me. I could not live that way, so I left to regain my sanity, my peace, and my self respect. Now, AH claims to be sober and to have "seen the light," but I have no faith in the lasting power of his words. In my opinion, leaving with the goal of getting your husband to change is a manipulation that is not likely to be successful. I think that because it has to be HIS decision to get sober, followed by HIS hard work to truly get into recovery. Unfortunately, you can't want it for him.
In my case, I believe the reason my AH is now claiming to be sober is because, for the first time, he's the one who is uncomfortable. He didn't want me to leave, and now that I'm gone, he's upset because now he doesn't have something that he wants. My fear, and the reason I won't go back, is that if his motivation isn't internal to HIM, then it won't last. He only views sobriety as a means to an end (me coming home), but doesn't see any other value in not drinking.
I hope that your husband gets sober, but you have no control over that. However, you DO have control over what you do, and what you are willing to live with. I would encourage you to be gentle with yourself, and start thinking about YOUR needs. When it's all about the alcoholic, it's easy to forget that you are a person with needs that need to be met as well.
I'm sure more people will be along soon with more perspectives and wisdom. Please keep posting, and hang it there!