I really feel for you. My husband suffered from reactive depression after our daughter was born (she's now 2). Like your husband he found a lot of his stress stemmed from work, also our daughter was a terrible sleeper which didn't help in the slightest. I too found it difficult to live with him at times and am ashamed to say that on a few ocassions I thought the easiest thing would be for me to leave him. We decided that he would take a break from work as my maternity leave was about to end. I went back to work full time (was hard at first as it was always my intention to work part time after having children) and my husband ended up taking over a year off work. We waited over 12 months for counselling, he had 4/5 sessions then his counsellor was ill and never called him back for an appointment - he's still waiting for sessions to restart 4 months later!
You sound like you want things to work between you but seem stuck in a kind of rut. The joint counselling sounds like a good idea - at least that way you can get an idea of what's going on in his head. My husband started running (on advice of doc) as exercise is a very good way to help overcome depression and it did go some way to helping him. He needs to know how much strain it puts on you looking after him and the kids - it's difficult not having the support of your husband - being a parent is hard enough.
We bought books and got lots of leaflets and self help stuff from the docs - don't think my husband wasinterested in any of that but I read it all and could then sneak the info into his head without him realising!
I hope things work out for you, keep us posted