Me? I went away for a long weekend!
My husband is a hands-on dad (2 kids from prior marriage) but we still had to work out our own thing with our own child.
The way to get them to do stuff is to stop doing it yourself. He sits on the couch, you sit on the couch. He doesn't make lunch, you don't make lunch.
Really. No one will starve. Let them HATE that there is no dinner, and let them eat cereal and PB&J sandwiches.
Here's a radical thought - let the kids NOT go to school one day because they weren't up and ready and dressed and fed. So what??? Really!! No one failed at life because they weren't in 2nd grade one day! It's dramatic, but it works.
The way low-wage workers got more rights is that they unionized, and developed standards. They went on strike. Go watch "Norma Rae" or any of a zillion movies on the Montgomery bus boycotts. You take away the workers, the management pays attention! You are slaving away as an uncompensated worker in your home while your "management" husband thinks his day is done after 8 hours. You have to stop.
Go away for a 2 or 3 day weekend. Don't take your cell phone (or at least turn if off and do not respond to ANY text messages!). Find a girlfriend or a sister or a mom or a college friend who needs to escape. Or go off on your own for something you would really enjoy - a bed and breakfast, a museum town, a beach, anything!
Tell your husband he's a parent and you trust him implicitly. Do not pre-make a zillion frozen dinners or give him a list of where the clean socks are. Don't food shop. He has a GPS, he can find the supermarket. He can figure out how to referee fights. The kids can figure out how to nag him that there's no toilet paper or that they need a permission slip for a field trip or help with homework. Honest to God, don't do ANY of this unless there is a severe medical condition and you need to tell him where someone's medication is! Otherwise, kiss them goodbye, get out of town, and go spoil yourself without guilt.
If you have to, calculate how many hours of extra sleep/relaxation your husband gets per week. Multiply that times 4.3 (the number of weeks per month). Multiply that times 12. That's how many hours you get, just to catch up for the last year.
Forbid yourself from feeling guilty. This is NOT your job! It took two people to make this family, it takes 2 people to run it. Let him run it.
Do not accept any BS from him. Tell him you have faith in his ability and his energy (since he's so well rested), and while you're at it, think about what standards you can relax. But by all means, let him function for a weekend! No one will die, I promise you, without a bath or a vegetable or a clean shirt. The only way to appreciate you is to live life without you.