My son is 10 months and we recently had a very, very serious argument on this topic. I had to sit my DH down and discuss with him exactly what we were both doing, pretty much minute by minute, really pinning it down to the specifics of each day and all our tasks. It was unevenly distributed and I was absolutely sick of him always weaselling out of that so I wrote it all out in black and white.
We both work, I earn more and work more hours, and yet I was doing one full day of childcare per week when we don't have daycare and he has one day free per week where he didn't have to do anything with DS at all, then I still did more on weekends. It wasn't reasonable and while he does the cooking, that wasn't balancing it out.
We were both very unhappy in the marriage - we've been together 12 years so it's not a new thing, but with the baby, yeah, it changes everything, and I feel that is so for most couples. We needed to have a talk because I didn't want to be with him anymore. I didn't feel that he had my back. That was it basically. He just didn't.
Luckily our conversation made things a bit more positive and we managed to negotiate that he will take DS for a full 5 hour shift on Saturdays, for example, and some other things. You do have to talk about it and I would suggest coming prepared with notes. However, it may be that in the end, it is not salvageable. I don't know that, but I do know you have to talk.
I wish you love and luck.