OP, I suffer from depression and I completely and utterly understand him not wanting to go out. There are times when I have literally wanted to stay in the house and go nowhere, and have stayed indoors for days.
However, and it is a big however, your husbands selfishness is still unacceptable regardless or not as to whether he suffers from depression.
At the end of the day, he can see all the mental health people he wants, but he'll never improve if he doesn't want to. It sounds to me like him thinking his issue is "more serious" than other peoples in the family means that he's taking on the role of a victim and as a result he's going to live by that and fuck how anyone else feels.
To be honest with you, I would explain how you feel, and I'd say that if it carries on you'll consider divorce because ultimately just because his mental health isn't good, doesn't mean yours should be dragged down with it while he gets to check out of the entire thing "because he's got depression".
Alistair Campbell actually wrote a great book about depression and handling it, he might want to read that. He's got you doing all the wage earning while he basically sits at home doing what he wants, and that is NOT a cure for depression. Going to the gym, eating well, sleeping well and believe it or not helping other people are good things to do for helping depression.
As my counsellor says to me: Depression wants you to be alone, it wants to stop you exercising, it wants to stop you seeing people, it wants you to indoors doing nothing all day. Your husband is giving in to the wants of his own depression so I wouldn't say he's making any sort of recovery at all frankly. He's enabling himself day in day out and that is not acceptable.
It's fair enough for a certain amount of time sure, but at this point it sounds like you are utterly frazzled and as a result I think some consequences are necessary if he refuses to leave the house and basically get a fucking life.