If housework is the only problem, then your problem is very easily sorted. My DH was very like this at the start of our marriage, and my mistake then was to expect him to see that he was being unfair.
I accepted that he was not going to do it, for whatever reason, and did the cleaning myself. But I stopped doing his laundry, I just did my own and the household stuff. I also stopped cooking, I'd either go to my mother for dinner on the way home from work or got something for myself (I'm veggie, he's not so it wasn't an openly hostile gesture as a dinner without meat for him is unthinkable). It took a long time but eventually he started doing stuff without me asking and we worked more as a team.
You need to get this sorted quickly though because you have a baby on the way. A very wise friend of mine, who knew what a lazy bastard my DH was, gave me great advice when I was pregnant with DS. She said when the baby came that I should be a bit helpless. It's my nature to be the one in control charge and I generally am very competent. But when DS was born and DH was home for the first couple of weeks, when he'd turn to me when he didn't know if he was doing something right, eg burping the baby, instead of showing him what to do, I'd say "god I don't know, what do you think?". This was the best advice ever because he didn't ever look to me as the number one carer. If both parents were present, there was no number one carer.
Also when DS was a baby, I thought clearly about what daily help I wanted from DH. I really needed head space each day so when he came home from work each evening, I handed the baby over and went for a walk with the dog. A small thing, I know, but it kept me sane. Also, his job every day was to make up the bottles at night and empty the dishwasher. That small contribution of time from him meant I didn't resent him. Another change brought in at that time was whoever cooked, the other person cleaned up after dinner.
FWIW, he's still a lazy bastard but a brilliant dad and a relatively good DH.