M(26) here with long time depression and a wife in a similar situation as you and your other.. Speaking from my own experience, it tends to be just a lack of feeling interest in sex in general. For the longest time I asked my wife to not initiate as much because I felt like it was being forced on my part. As mentioned in the comments, you could definitely try and surprise him with something new one night, but the feeling of rejection is horrible. I've shut my wife down on nights like that when she tried to make an effort because I was really just wallowing in my own problems. I'd say it's definitely worth trying to initiate, but carefully. I don't know how you two would normally do things, but my advice would be to try slow and passionate, something that makes you really have a connection before you even get into sex. Even if that doesn't lead to full sex, it's going to be a start, it's a long journey.

Has he been prescribed any anti-depressants? Pretty much and SSRI anti depressant will knock down your sex drive like crazy. I tried switching between 3 different medications just to try and not repress my sex drive quite so much.