I've never heard of a shift swap due to medical reasons, but I haven't worked half as long as some people on this board have. I wouldn't say it's impossible. Not knowing how his department works, only he can find out whether or not that's possible and it's ultimately dependent upon them to allow it. I'm asuming that he already knows the answer or doesn't want to ask his employer, otherwise you wouldn't be here. You can't ask on his behalf.
What you've described is not a medical condition unless he's depressed due to a chemical imbalance that's controlled through drug therapy. While there are well-documented physiological responses to living and working outside standard 'day shift' hours, I haven't heard of shift work affecting 'brain chemistry'.
If his psychological issues are affecting him as much as you say, he should check into taking a leave of absence and get REAL treatment. There's also a big difference between a 'therapist' and a clinical psychologist and marriage counselors are not qualified to treat psychological disorders. If he so chooses, he needs to see a psychologist, not a counselor or therapist. If he's found to have or believed to have some sort of neurological chemical issues, he can see a psychiatrist which is able to prescribe medication and remedy the problem.
I hope he gets the help he needs and gets past his issue as soon as possible for him. Good luck to you and your family.
Of every one hundred men, ten should not even be here. Eighty are nothing but targets. Nine are real fighters, and we are lucky to have them, for they make the battle. Ah, but the One... One of them is a Warrior... He will bring the others back.
"Wrong door, buddy!"
Let no man's ghost say my training failed him.