Agree with posters saying coparent! Dh has always just got on, he does what needs doing.
Things are a bit different for us as Ds is 1, but back at the 10 week stage he was struggling with reflux and it was a tricky stage. Dh would get up at 5, walk dog, get lunches, make breakfast, clean bottles, get ready for work. Then I got up, he would tend to baby while I showered, ate, dressed. Then he would go to work. When he got home he would take over with Ds, Ds at the time never slept for long so I went to bed at 8 and Dh stayed up with baby til 11.30 so I got solid blocks of sleep.
Now, thankfully, Ds does sleep but we alternate who gets up if he does ever wake, and each of us gets a lie in either Saturday or Sunday. In the evening, one of us will feed, do bedtime with Ds, the other will wash dishes, do bottles, cook, clean up. We alternate this too as putting Ds down is easier.
The main thing for me is that I never have to ask Dh to "help", he sees it all as part and parcel of being a dad. Is there a chance your Dh is a bit apprehensive about doing things wrong? It's still early days after all, he might just assume you know better.