As the oldest of a big family who has observed a lot of this, here's my 2 cents. (sorry if I'm resurrecting the thread!)
It's actually really important that your husband and your boys spend time together. There's a guy thing there (I don't completely understand it either!) where boys need a male role model. If they can't look to their dad as a role model and imitate how he does things, and if they can't copy their dad when they're trying to act grown-up and masculine; they'll wind up looking for role models in popular culture. I know a lot of guys my age who never really spent time with their dads and many of them are copying characters in movies, searching for that role model. It isn't a good thing because those kids pick up immoral attitudes from those actors they imitate. That's part of why there are so many school shootings, teen pregnancies, problems with drugs, etc. Someone copied the wrong movie character!
Listening to your description, I think Dad's trying too hard to fit into your role. Maybe Dad knows he can't be the perfect Mom and he's worried about that? I think it's important for him to understand is that things should be a little different under Dad than under Mom. If Dad suggests ham and crackers instead of an elaborate casserole, that's fine. (Also, if son doesn't like what Dad cooked, that isn't Dad's problem. It's the boy's problem, because he chose to be a picky eater.) I think in a lot of well-balanced homes the parents interact with the kids differently. The house rules still stand but the parents cook different things, have a different attitude, do different things with the kids. That's ok, and maybe your husband needs to realize that.
Do keep in mind that guys get tired too, though. Check and see, "I don't want to babysit all afternoon" might mean "I know you're tired of being stuck home with a toddler but I need a break too! I've been working and listening to kids squabble for weeks and it's time for me to get out of here and go fishing!"
God bless you,
Grace