Oh, I feel for you.
I definitely feel that some rules need to be established. Things like, everyone (except the little ones) should be responsible for washing their own clothes, and should help with preparing or cleaning up after meals, and should pick up their things in the house.
If you're doing all the extra work that the teens are generating, and your husband is relatively free of the extra work, then DELEGATE! If he is having to work extra hard cleaning up after them, he might be more willing to establish rules.
You might want to go to what we have called the "Elizabethan System." Everyone has their own plate, bowl, fork, spoon, glass or cup, etc. And everyone is responsible for keeping their own plate, fork, etc., CLEAN and PUT AWAY. Everyone has a designated location to store their items. Put all other dishes in boxes temporarily, until all the adults (or almost adults) have the habit of cleaning after themselves.
Maybe you could establish certain nights that the teens are responsible for preparing supper. For example, SD cooks on Tuesday evenings, and SS cooks on Thursday. And please, make them both do it - that boy needs to know how to cook if he is ever going to live on his own. You may have to teach and oversee them until they are able to do it themselves (including how to wash dishes). And I know this is harder than doing it yourself, but like you said, you're afraid they're going to be a drain on you forever.
It sounds like you may have to teach these two the life skills they need to survive on their own (like cooking and cleaning and contributing to the household). Their mom didn't teach them, and your DH seems to assume that they already possess them.
You might want to take the girl to a doctor or family planning agency to make sure she knows birth control and STD facts. And breaking curfew must have consequences.
OK, I'm having a bad case of insomnia, and I'm in a bad mood. But I think your husband either needs to help you establish rules and enforce them, or HE needs to be the one that has to clean up these almost-adults' messes.
Can you get your husband to a marriage counselor? Maybe if you talk about it with an impartial third party, he might be more likely to see how this intolerable situation is affecting you.
Good luck, and post back here to let us know how things are going.