J.,
I think it's great you have a routine. But where do the husband and kids do their share?
A 4-yr old can perhaps set the table. Your twins can help their sister. All three kids can pick up stuff off the floor. Barney has a "clean up" song kids love (works better for my sitter). Right now having your kids helping will take longer to get things done BUT in a short time they will be able to do small tasks giving you a little free time to do something else. And if you can get them to clean up eventually the piles around the house will decrease (I'm still working on this at home myself). The important thing is that everyone contributes to the "home." Everyone can do something that helps the family no matter how big or small.
As for a clean house, well maybe you can let a little go. Figure out what things are a MUST DO and what cleaning things you could do every other weekend. Make a list of what must be done and ask your husband to help with half. Maybe you can think about reducing your kids toys, don't throw them out just put them in the closet and swap them every so often. It would be less clutter to keep up with and they toys feel new and fun.
Go to the thrift store or Wal-mart and get a crockpot. You can check cookbooks out of the library and try recipes. Then you can plan to use it 1-2 times a week. Put it on low before you leave the house and turn it off when you get home. If that's too long you can plug it in (on high) as you cook a regular night meal then the next day reheat the crockpot meal in the microwave.
Try freezer cooking. Usually it doesn't take any more time to double a recipe when you cook. A great website to visit if you want to try freezer cooking is www.30daygourmet.com They have tons of recipes, e-cookbooks, etc. The idea of freezer cooking is cooking for one day to feed the family for 30 days. There is also a email digest on yahoo groups whose members trade recipes and advice (____@____.com) also they can give you info on what won't freeze like mayo. It comes down to planning ahead, I'm horrible at planning so I usually just cook for a few hours instead of a whole day or just double recipes. Even if you decide it's too hard cooking a few things or prepping a few things on the weekend would make weekdays easier. You can also try this with a friend. She cooks a few things and you cook a few and then you trade. Think of it like a cookie swap. You can compare what you spent and split the costs in the middle.
Maybe you can consider occasionally having a quick but not so healthy meal like fish sticks and tater tots. Add a big salad for some vitamins. It's great to have dinner on the table in 25 minutes after you get home. And the kids are almost guaranteed not to complain and eat happily.
Also if your husband gets home before you can you let him start dinner and take over when you get home? Or let him cook. If he doesn't then maybe he can learn. Try the book A man, A can, a plan. If you don't mind all the canned stuff it's an easy way for Dad (or Mom) to put dinner together without knowing much about the kitchen.
Do you know any young family where you can trade babysitting? You take their kids for a couple hours one weekend and next you switch. While you're kid free you can study, clean or relax.