Welcome to SR 1datatime. It seems like your husband is willing. The best thing you can do is be hands off and let him find his ground. Hopefully sobriety will click.
Do you have any support for yourself? Are you attending Al Anon?
It can be very lonely living with an active alcoholic and the ongoing anxiety can also be unbearable. Even though your husband is not mean, I d bet that you are worried to death about his health. Also, a pattern among family and friends is that we make the alcoholic the center of our world and forget to take care of our own emotional (and sometimes physical) needs.
It's like life revolve around their addiction and the ongoing or upcoming crisis brought by it.
We have a section for friends and family members on SR and you will find a lot of support there. You will also of course get support in newcomers from alcoholics in recovery and people like me who are in recovery for both alcoholism and codependency.
Here is the link to the F&F forum. I look forward to seeing you there Friends and Family of Alcoholics - SoberRecovery : Alcoholism Drug Addiction Help and Information
Ps: you will hear some horror stories there, try to identify with the feelings (anxiety, resentments, hope) and not compare. The same way that some alcoholics have "high" bottoms while others end up in the gutter, not all F&F go through the same harsh stuff but the root of the problem and some of the emotions are similar.