As hard as it may seem from your (very understandably) frustrated perspective, I'd explore with him whether he's willing to seek assessment and maybe therapy for depression. He's getting more than enough rest, and his current behavior doesn't seem like himself. A new baby often brings up unresolved experiences that can trigger depression or anxiety responses, so that people are at their worst at the very moment they'd like to be at their best. Wishing you and your family health and joy.