He is basically dissatisfied with all the normal annoying, relentless, daily aspects of being a grown up. With a perfectionist streak and very high standards ((the tidy binges). And a childish passive aggressive approach to dealing with all that (huffing under breath), whilst not so secretly blaming you.
You say it's spiralled over the past few years. Was he like this before and it's just more excessive? Was he like this before you had children? Has he always been a naturally negative person, a bit 'glass half empty' and it's just an escalation of that?
Also as Attila asked, how does he behave around other people - is he negative in outlook and irritated by them too?
It would be unusual to such behaviour to spring out of nowhere so I am predicting you will say yes he was always like this but that at the start it wasn't as bad/it didn't bother you as much. If it really is a major personality transplant from a certain period of time then can you identify anything that happened to trigger it? It's possible (but less likely) that he's got some sort of depression/disorder going on that means he is finding life overwhelming or pointless, but from what you describe that doesn't seem to be the case.
In which case it's probably an ingrained trait. He's aware of it but chooses not to resist or try to change. Even more so if he is not like it around others, so more indication it's something he can choose to control but doesn't around you. He's also not adjusting to the natural state of a hours with kids in it and all the extra tasks that go with them. My ingrained trait is to be messy, combined with a lazy streak when it comes to household chores. I control it as best I can, especially when living with others, and if asked by partner to tidy up then I do without moaning. That's my choice.
As for what to do about it, you could try a grown up Adult to Adult conversation where you calmly explain how you feel, what you need, and work together on solutions. But I suspect it won't work. Because that requires him to accept he isn't behaving logically or reasonably and to commit to change.
As for helping you cope, well in the short term you can find techniques to ignore him, pull him up when he's being ridiculous, let it wash over you more, live more separately to avoid the moaning etc. But that's not sustainable long term and hardly recipe for a happy long term life. For you or for your kids.