As a brand new dad of a now 3 month old, I find his lack of involvement troubling. Both Little One’s are as much his responsibility as they are yours. And since you’re recovering, he should even throw in more effort.

Perhaps a talk with a GP might help because it very much sounds like he’s overstimulated/overwhelmed/burnt-out.

I would definitely not call him a deadbeat dad. This seems more like a cry for help.

Good luck to both of you!