You are not worng - you do need to sort this out before the baby comes along, because there will only be MORE jobs to do, not less, and you both need to work as a team.
If you are breastfeeding, or responsible for doing night feeds, you will effectively be on duty 24-7 to his 12-hour shifts 'at work'.
I'm afraid this attitude of his probably went some way to contributing to the breakdown of his previous relationship with the mother of his children.
You do need to take the heat out of it though.
You're leaving stuff for him to do to make a point.
He's making the same point back.
You're just going to be at stalemate.
Start over. Explain it's not so much having to pick up most of the chores whilst you're heavily pregnant and knackered, but that every time he makes EXTRA mess (like leaving the stuff on the side in the kitchen instead of putting it in the sink, or not wiping the spitty toothpaste, or leaving his dirty underwear on the floor) then it feels like he is saying "Fuck it, Liveinmaid can do that." Which is disrespectful because you are not a maid.
Divide actual chores - weekly cleaning, laundry, etc - between you, with you picking up more than him for now, because you have more time.
But insist that new mess generated by him or the children - avoidable mess, stuff that is just part of being a good human being who respects living with other people - is cleared up by the person who made it.
In my house, over the age of 2 or 3:
No one should have to take someone else's plates or cups to the kitchen.
No one should have to pick up someone else's dirty laundry off the floor.
No one should have to put away something someone else has been using (toys, hobby stuff, whatever).
Of course as a parent you help smaller children, and you do a lot of "reminding" and sometimes a fair amount of losing your shit about it but basic principles should be that people put stuff away, not just put it down.