My other advice is to click this link and then practice the conversation before you have it https://dbtselfhelp.com/relationship-effectiveness-give/
Some thing that helped us was we both sat down after the LO was asleep and we made a list of everything we did that day. Then we showed each other our lists. This helped get the point across that in a day I do a lot more than he realizes. Then we talked about how we could even things out. We came up with the idea that anything that has 2 parts are something we both do and divided up the rest. So an example would be groceries: he picks them up and then I put them away or dishes: he loads the dishwasher and i unload it or laundry: he washes and dries I spot treat and soak everything and I put it all away. I also have several crock pot meals that I put him in charge of so I don't always have to make dinner. I make my LO lunch the night before to help the day go soother.
First things first: Get on the list for daycare!!! Just get on the list! You can always back out but it takes ages to get in.