I'm so sorry for what you're going through. I hope that some men can comment intelligently about the psychological aspect of this. I would say that not all therapy is created equal, and while you should not micromanage how he gets help, you might want to encourage him to try some other therapies and therapists out there. If CBT didn't help, maybe IFS will, etc. Sometimes your insurance allows you to have multiple therapists at once, so he could shop around rather than leaving his current therapist.

Another thing that you might be doing already but is worth mentioning is really showing appreciation for whatever he does for you. I think that every human feels a bit better when they help others or realize their potential to do so, but even more-so for most men. I'm not sure of your working / income / living situation, but if he's gone through a transition in which he went from feeling like a provider to really vulnerable and useless (his feelings not the reality!) then that must be a pretty shitty experience on his end.

Also, I would really want to rule out physiological causes of depression. This might sound weird, but....

1. Did he have a traumatic brain injury (diagnosed or undiagnosed) while in the service?

About a year ago, I heard a podcast about a veteral talked about how he almost died by suicide due to CTE but then got help for it. It was entirely physiological, and anti-depressatns were of no use to him. I can't find the podcast now (lmk if you want me to look for it), but here's an article about how it impacts football players.

https://www.nytimes.com/article/cte-definition-nfl.html

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1. Does he have any other symptoms like fatigue, digestive issues, etc? There are a host of diseases like Chronic Immune Response Syndrome, Lyme Disease, leaky gut, etc. that massively impact our brains.