My DH was pretty similar, he would come home from work and demand "me time" after I had been dealing with a refluxy baby that didn't let me put him down all day, even when asleep (but hated the sling). I was pretty blunt about telling him to shape up, and he did, begrudgingly. He honestly seemed to be completely delusional that I spent my days napping and watching tv with a baby on my boob - he thought he had it harder and it was only with time, lots of discussions and after my days really did get easier that he has pulled his finger out. Now he is the most amazing dad, he does the entire bath and bed routine every night and also gets up for all the night wakes.
Are you breast feeding? I found that made DH feel a bit useless in terms of settling bubs, also I was a bit bossy because I felt I knew DS better than he did (knew his cries etc), we were both completely out of our depth but maybe DH felt he couldn't really help much anyway, is it possible that's what's going on for you?
I hope things improve. You can always hand your DS to your DH and just say "I'm having a bath, deal with it"