I know how you feel. However, are there things that he takes care of that you don't- like oil changes in the cars, repair work, lawn mowing, shoveling snow? My husband does these things at least.
Some things you do have to let go. Four bathrooms are a lot to clean. I have 3 and it is hard to keep up and my kids are grown up! So, close one off, tell them it is off limits b/c it is too much cleaning, or even 2 of them, use only when company is over. If the dusting can wait, let it go 2 weeks. Mop the kitchen every 2 weeks. If you are all gone during the day, it can't be all that bad.
It took my husband a long time to learn to pick up his clothes and trash. And my sons are bad about it too.
Don't let your sons get away with things just b/c your husband does it. "You don't worry about what Dad does, just do what you are told".
If you have scheduled times for doing things, like Thurs night groceries- ask you husband "please wash up the dishes, counters and table while I am at the store". That way the kitchen will be cleaned up. Or make a list and ask him to do the shopping.
You can put you and the boys on a schedule of cleaning the bedrooms and bathrooms, etc, but men like don't like to be told when and what to do. Keep a running list of extra things that need to be done- like cleaning the fridge, sweeping the garage, washing the windows, cleaning out a sink drain. Ask him to please help out with these. Then, don't discuss it and don't do any of those things. Just leave the list hang on your fridge or a cabinet. When people come over they are going to notice it and comment on it. Then you can explain that this is your husbands chore list. Date the day you put the chore on there, so it doesn't look like you came up with it all at once.
If he doesn't cooperate, then do the best you can with the boys' help. Make a habit of picking up his things he leaves laying around and put them next to his side of the bed or just get a laundry basket and put it all in there- beer cans, trash, clothes, shoes. He can sort it out when he wants.
Make sure you make time for you and your husband to go out. Remember, when the kids are gone, it will be you two alone again and you'll want to have activities you both enjoy.
Maybe your husband is tired b/c he doesn't get enough exercise. Or if his job is physical, maybe he just needs to rest 30 min when he gets home. Eat out on Fri or Sat evening so you don't have kitchen clean up those days.
You could put him in charge of the checkbook, paying the bills and then threaten to quit work if he doesn't help out. That way he can see how much money you have and what the effect will be if you don't work.