[Oops. I didn't intend this to be so long. But it just started pouring out...]
I am really really struggling with my husband's grumpiness, to the extent that I often feel a weight is lifted when he leaves the house. 
He has a naturally pessimistic outlook on life, and will always make a negative remark if I comment on something or if I get enthusiastic about something. Everyday things can trigger miserable moods that last for hours and hours. He isn't clinically depressed, but is I think just chronically dysthymic. I don't think he has ever felt joy or excitement. He wasn't so much like this when we met, because our lives were much easier then.
It's true we have some stress, but our lives are comfortable and pleasant compared with the problems most people on this planet face. Yes we have toddler twins and a crazy house that is hard work to maintain. Yes his job is stressful (but so is mine). But honestly, our lives really could be a LOT worse. I do all the night stuff with our insomniac twins because he can't handle sleep loss, but then he gets grumpy because he feels guilty that I'm doing too much!
We do work well as a team in our house. Although I do almost all the child stuff, he does more of the domestic stuff, which suits both of us. We're both behind with our 'to-do' lists, but he is completely tyrannised by his: if I suggest we might do something as a family for once (gobsmacked emoticon) I'll get a 5-minute stressed lecture about how much he has to do.
I have tried to talk to him. I have told him how hard I find it. Sometimes he apologises which is lovely, but once that's done, I'm just waiting for the next mood to start. One night he came home, gave me a hug, and told me he wanted me to take a zero-tolerance approach to his moods, but the next night we were back to business as usual.
Almost everybody gets a bit grumpy sometimes. But this is so extreme. I can put up with lots of things in our relationship (eg no sex) but the moodiness makes day-to-day living hard.
It doesn't help that our beliefs are different. He thinks it's normal to not make an effort with your nearest and dearest. I was brought up by two mildly depressed parents and even as a child, I resolved that I was going to make an effort to be friendly to people close to me as well as to everyone else. Also, I have a job in which I have to be very emotionally calm in the face of sometimes highly emotive/unreasonable behaviour. He, on the other hand, admits that he snaps at people at work!
The last straw is that he has just been on a short holiday with his friend, which is completely fine by me. (She's lovely and can often talk some sense into him!) But instead of coming back refreshed, he's come back GRUMPY!