I have 2 strategies that mostly work (my kids are about the same age as yours).
1 - give them at least 1 chore that affects them, and then no matter what, don't step in when they don't do it. In my house, this is their laundry. I don't do it. They both know how to operate the washer and dryer. If they run out of clean play pants to wear and the only clean pants they have are jeans, well, then they have to wear jeans to school (my kids hate jeans). If it's "wear a red shirt to school" day and they don't have a clean red shirt, then too bad, they can't participate. I don't fuss at them when their dirty clothes pile up in the hamper, but I don't take responsibility when they don't have something they want. If they complain to me, I just shrug and say "I guess you should have done your laundry this week." Natural consequences. (I do step in to prevent them from wearing dirty clothes because they would probably do that if allowed LOL).
Obviously this doesn't work well with things like clean bathrooms and kitchens because they would live in filth before it bothered them, so that brings me to
2 - family clean-up time. Unless there are extenuating circumstances, I don't clean up by myself. After dinner, younger kid clears the table, older kid loads the dishwasher, I package up leftovers (husband usually cooks so he gets a pass). On Saturday mornings, anyone who is home helps with cleanup. We go room by room - kitchen, bathroom, family room - working as a team. I think this works because kids this age do still need direction and I am right there to get them back on track if they get distracted. As I'm putting leftovers away, I can say to my older child "you missed the spoon next to the stove" or to younger "great job clearing the table, wipe it off and you are all done" or whatever.
This doesn't work perfectly, especially during our peak sports season and we have weeknight practices and no one is home on Saturday mornings. But it helps.
ETA: I just re-read your question and have a comment about your husband. Do you ask him for help before you get so frustrated that you are angry? I know I know, he should SEE that everyone is helping but him. He's not a child and he should know to step up. But personally, I'd rather just say "Hey, honey, we could use some help here" as soon as I start to feel frustrated instead of letting it build until I boil over.