In my experience, I have been suicidal. The only thing that stopped me was my belief that my youngest daughter would not be able to handle it. That was on and off for a couple of years. Once it was so bad I hospitalized myself.
The rest of the last 9 years I have been suffering from treatment resistant depression and some other things. I do want to die. I find myself being jealous of people my age who have died. I wonder why 2 of my former co-workers died from cancer when they wanted to live and I don't. I do believe in heaven, but even if I didn't I would still welcome being told by a Dr that I had a fatal disease. But, I am not going to take action to kill myself. It's hard to explain, but I agree with your husband that they are two very different things.
If I were in your shoes, I would ask that he let you know if he moves from wanting to die to being suicidal.
Sobriety would help. I am 29 years sober thanks to what I learned in AA. Maybe your H would consider going to a few meetings? It is non-professional help by design.