Xena, I have a good relationship with my DH generally but you could have been describing a Saturday morning in my house to a T {The detail was freakily similar). DH has always acted as if the kids are my job, and has called me out of the shower before and then gone in the garden for a cig. We also are moving house! In fact he just called me to get DS2 off his leg and has sat down to read the paper.
There is no easy answer. Some dads are brilliant at taking their share and others aren't, but I found that stress was a huge factor in our bust ups in this sort of situation. My DH does work hard all week (although so do I) and I have just kind of accepted the situation. The minute I stopped getting upset he generally got a bit better, and he does help out a bit more now. I tend to get on with it but negotiate little breaks for myself.
I would just get on with it for now but tell him you are going to have a lie down later on when the younger ones have a nap and wait until a less emotionally charged time (in the evening over a glass of wine in the garden?) to tell him he really must do more to help. I am sure he knows that he is not doing enough deep down.
My moment came when DH told me he wanted another baby and I told him (in a nice way) no way, because I would have to do all the work as I do now. He told me he would help out more, so at least he acknowledged it. He does help out more but neither of us are really stressed at the moment either, which helps.
When I see really hands on Dads and get a bit jealous I just remind myself that if ever we split (and believe me I hope that never happens and am sure it won't) he wouldn't stand a hope in hell in a custody battle....
I just also remind myself that although he is not the best at helping out with the kids, housework, etc, DH has other really positive traits that maybe a more hands on dad wouldn't have. hth.