I don't know what your counselor recommends, but I would start with making your kids, who are plenty old enough, be responsible for absolutes. I don't know how much they do in your house to contribute, but I have a feeling from reading what you wrote that they don't do enough.
Each week, rotate a jobs list. Make each kid do the same jobs so that they know how to do them all. There is NO forgetting - if it's their week to do the job, they DO it. The two older ones are grownups now - they have no business living "off" of mom and dad. They need to be held very accountable.
As for the rest of your husband's bellyaching, I would ignore him. If you pick up a book everytime he starts, or start humming to yourself, or leave the room, he's just complaining to dead space. That's what he needs. However, he'll have less to complain about in the first place if your kids are doing their jobs.
Your husband is not the only family member to say 'where are my clean shirts', by the way. The kids should be doing the laundry and that should include Dad's shirts. It's part of the "payment" that they owe for still getting to live with you at 20 and 22.
I'm not saying that your husband has a right to do all of this complaining. But with 2 grown kids still residing in his house, there shouldn't be dirty dishes and dirty clothes. There just shouldn't be. Hold your kids accountable, J.. THEN you can start holding your husband accountable for the things he won't do.
If I were you, I would HIRE someone to come in and do the house jobs that you and the kids don't know how to do. SO WHAT if he doesn't like it? If he won't commit to painting a room, go ahead and do it yourself or hire it out!! Ignore his fighting about it. The sooner he understands that you will take the bull by the horns and have something done WITHOUT him, the sooner he'll either do it himself or get over the fact that you'll have someone else do it.
This is your house too, and you have the right to maintain it whether it's with his help or not. That's pretty much what most wives do, J.. Not all men can paint or repair. Lots of men don't want to pay for it to be done, but that's just tough. If you have enough money in the budget, you should do it.
These concrete suggestions won't fix your husband's attitude, but you need VERY MUCH to do these things anyway. Grown children shouldn't be living under your roof without doing housework, especially what your husband finds important. Lay down the rules and make them stick.
Good luck.