Yes, I do believe that you should support each other in marriage.
Does he support you emotionally? Obviously not physically.
I would be more concerned of his constant isolation of "himself", hiding in the bathroom, the thoughts of harming himself, the addiction to the gym, a place to escape.
It's sad what vets have had to go through, breaks my heart. So many do come out with mental health issues, breaks my heart.
Support. And, help him find ways, to help him over his mental heath issues, and hopefully in return, he can find solace in his relationship and prefer the arms of you holding him, instead of hiding in the bathroom.
Instead, of worrying about cheating and providing him with more issues to deal with.
With cheating, you will find out, eventually. All do. And if that occurs, then you can make the management decision to stay or leave.
Worrying out it, will eat you alive and at the same time, provide more anxiety to someone that has his own issues.
Worrying out it will not solve the problem.
Finding ways to have your Husband have something to smile about again, however, will solve some of the problems to your marriage.