I agree that your DH should consider talking to - not a therapist - but a psychiatrist. I think it sounds more like bi-polar disorder than depression, and between those two it's really important to get a correct diagnosis.
Being married to someone who suffers from a mental illness is very tough. And honestly, if he's going to fix it, he needs to first realize that he needs help. A couples therapist for the two of you is great, but it will *not* help if he is suffering from something like bipolar or depression. Or rather, it might help - when he's feeling good - but it will do nothing when he's not. Long term mental illness is typically caused by something physical - often a chemical imbalance in the brain - and won't go away without addressing the physical side of it.
My DH suffered from untreated depression for years, long before I ever met him. Whenever he got overwhelmed with life, he would go out and do stupid and destructive things. It escalated until he left me, and then finally hit rock bottom. Only then could he really see what he was doing and get help. After that, we had some long discussions about him getting help for him before we even considered whether he and I had a future. I had and have no interest in being his babysitter or his nurse. He got healthy, and then we worked things out between us. He still backslides some times, or things get overwhelming, but now we can talk it out and work it out as a team.
Anyway, that was a big ramble, wasn't it? My point is that I DO believe things can work out, if you both want it to and you both are honest and up front about your problems and getting help for them. I also believe that you're right to block out the negative influences during this time. There are always ots of people around who will delight in telling you how awful he is and how they always knew this would happen. How helpful is that?It's not! And my worry would be to make sure that your family is not making nasty comments about your DH to your children.
It really bugs me what your husband said about not being happy when he's at home. I mean good grief, is it really that bad to be with your wife and kids? I see your kids are really closely spaced too. That might be part of the issue. DH and I went through a rough patch after our 3rd back to back baby (3 of the 4 are every 2 years). It was just overwhelming to him, which irritated me because that is what HE wanted in the first place.
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