1. They can drink. 2. They can join AA and work the program.
Well...I'm from the alcoholics' side and I also fell into codependency in my twenties. "Double Winner," as they say. Alcoholism in my family.
I didn't "follow" AA or Al Anon or work their program per se, but I feel I've recovered from both. If you read around the alcoholism side, there are many paths to sobriety and AA isn't the only one. However, I do agree with you that some ongoing work needs to be done - for all of us. What that looks like is highly individual.
Hope1111 - I hope for you that you will find a way to get some time away from him, whether that's a day with your friends, a week at a hotel, or a permanent break. Your husband has to want to be sober and right now he doesn't seem to want that. Depression, anxiety and low self-esteem are all exacerbated (or even caused) by alcohol, but it's futile for you to try to fix that.
Stick around and keep reading. Welcome to the site.