I am a recovering alcoholic. I am the only one that can say that. In my experience it is only the alcoholic who can say they are an alcoholic. It really is up to your husband to tell people he has an alcohol problem, no one elses.
What you could consider is telling others that he is pursuing other opportunities and leave it at that. The details are no one elses business, in my opinion.
I hope the very best sobriety has to offer each of you! LOL