Not all men are like your husband. But I'm not sure there is anything "wrong" with your husband. He's like a lot of guys I know. But again, like you, I'm not the "normal" guy either.
My wife's pregnancies did not diminish my sex drive, except around the last month or two when she was quite large and seemed physically uncomfortable. I was perhaps a bit too afraid of hurting something. But after the pregnancies I was ready to go again. But then I've always had a much higher sex drive than her. I've always wanted it about once a day, on average, my whole adult life, and I'm now in my late 50's.
And you want to jump his bones when all the chores are done?! If only my wife could be like you -- I'd be the happiest man on the planet!
Can men get post-partum despression? I don't know -- I never had it. I'm known as the guy who's almost always in a good mood. I thought my kids were the cutest things I ever laid my eyes on. Picked them up and played with them all the time. They gave me energy and enthusiasm. Never got tired of them.
And I got up several times a night to change the babies and deliver them to my wife for breastfeeding.
If my sexual functioning were to drop off, I wouldn't hesitate to see my doctor, who is, by the way, a younger female.
My wife is a superwoman professionally and at home, and also fit and attractive. She works out all the time, as do I. Doesn't intimidate me at all. In fact, it turns me on.
My wife would never have allowed me to behave as your husband did, especially with regard to not helping with the baby at night, etc.
He didn't help with the baby, you're a superwoman, you want to jump his bones, and you want to give him oral sex? Wow, you seem like a dream to me.
As for getting him to a doctor, tell him you'd like to go to a doctor or sex therapist with him to discuss the matter. And tell him you'll go alone if he doesn't come along. Some men change their minds when they realize they are going to be the subject of discussion and they won't be there to "defend themselves".
