SO with PPD?

My LO is almost a month old. I had a horrible pregnancy and a horrible delivery both with severe complications and I'm on bed rest still recovering. We moved in with my mom for additional help. My SO only got 2 days off for the baby and works in NYC every day and is gone 12 hours a day. Recently he seems really withdrawn and doesn't talk much. He take care of the baby when he gets home and at night but is convinced the baby doesn't like him. I try to celebrate the small victories with him like when he smiles or when he giggles at my SO it doesn't help that my sister just shrugs it off saying well he does that for me all the time. Is there anything I can do to make him feel more of a connection with his son? I feel awful. He's admitted he is jealous that I get to spend all day and night with him.