M.R.
A couple of things that might help. My husband is also home days but he works evenings and is in school half-time, so he "works" 2 full-time jobs (child care, 1/2 time work, 1/2 time school) and I do the same--work days and watch the kids when I'm home. Our only family day home is Saturdays. I still am driven insane by the house and sometimes by my kids diets (I don't think they know what lunch is if it is not PB&J sometimes) but I am also exhausted by the housework on top of everything else. I was frustrated that the kids would watch a lot of tv when I was at work, but on rainy days they go nuts stuck inside, etc.
Some things that helped:
Offer to set meals and snacks up ahead of time. (I did not want to take the time to do this, but said something about making healthy food handier for meals if it was set out, even if it just meant a cup of diced fruit was in the fridge by the sandwich bread and milk as a reminder.)
I had to learn to relax about the house (a bit). Try sitting down and making a priority list. Your priorities with house work are not your husband's. What are the top five things that make you nuts when you get home? Dishes? Wiping off the dining table? Smelly trash? The litter box? Tissues all over the coffee tables? (this is sounding like my house now...:) Tell him that if he and your child can start making a habit of doing a 10-minute overhaul right before you get home, it would mean a lot to you and you could relax and enjoy your time home a bit more.
Decide what major cleaning must be done and how often. I can't remember the last time our bedroom was clean--we don't hang out there, entertain there, or eat there, so it is no longr a priority (I wish it were, but...). Our priorities for health and safety reasons are vacuuming our living areas, washing dishes, mopping the kitchen, and wiping down the downstairs bathroom at least once a week. Pretty pathetic and basic, but it makes life livable. I HATE seeing empty boxes on the counter, or grocery bags on the table, but I am learning to just pick them up and move on.
We have been doing this schedule since before having our now 3 1/2 year old and to be honest I still get cranky and frustrated over the house and the kids sometimes. I have to step back and remind myself that most dads aren't watching their kids full-time and doing everything else he's doing. You are working more hours than I do, so you do need to designate a few tasks specifically, but if it is something he doesn't even see needing to be cleaned, you are not going to get him to do it regularly. You've got some negotiating and compromising ahead of you, but it can be done.
Oh, and our kids are still on a late-to-bed, late-to-rise schedule since my husband's work shift ends at 11, so 12:30 a.m. is pretty normal in my house, but they are getting plenty of sleep. Is he sleeping late enough and they are just on a late-to-rise schedule? Anyway, kids are, thankfully, adaptable! :)