Well, my kids are 7 and 11, so I can pretty much do all of the things your DH can. I remember, though, when I just had the one child who was 3, and we were ttc #2. My husband decided to get LASIK. After the surgery, I had to go pick him up, and his prescribed course of treatment was to take this heavy sleeping pill so that he would sleep all afternoon into the next morning. I was also looking into getting LASIK, but I had just found out I was pregnant, so I couldn't do it at that time. I remember feeling envious of his sleeping pill, and I wished I could get the surgery just so I would be told to take a sleeping pill and sleep for the afternoon. But then I was still nursing, so I knew I couldn't do it anyway.
I did have a chance to sleep in, however. As soon as my babies were of an age where they didn't have to nurse constantly, nor did the need me all the time, I split up the weekend mornings for sleeping in. DH always took Saturday, and I took Sunday. It depends on how sick I was, but if I was vomiting or had a fever, and I couldn't really function, heck yeah, I went to bed and let DH shoulder the burden. I've had back problems on and off, and there was a point in time where I could barely get up off the bed. He did bring me my 2 year old to nurse at one point, but he did the care.
The only thing I feel like my DH can do that I can't is not do things for the kids that involve his time, and not feel guilty about it. If the kids get invited to a birthday party and I can't take them, he won't take them, he says they don't have to go. He didn't get to have birthday parties when he was a kid, and he thinks all these birthday parties and children related events are way overdone. So sometimes I have to rearrange my schedule and do a lot of running around if I want them to go. I guess because he works long hours, he is obsessively protective of his free time. I don't really feel like my free time is my own. I do a lot of out of the house activities, but he can just sit in the house and not have to do kid related stuff.