I have been in an even worse position than this (me full time, DH at home with kids mostly at school/nursery, and a cleaner), with me still spending evenings and weekends doing a lot of the household stuff. I changed it, but it took time. Basically, every couple of months I would explode/breakdown and there would be an improvement. Over around 18 months - 2 years, it got to a much fairer place.
While this was all going on, I found someone who would come for half a day every weekend and I used that time just for me (often gym). This was my lifesaver. It was ridiculous, but worth it.
Also, have you 'outsourced' everything you can/can afford to and simplified as much as possible (simple, weekly meal plans?)
Somehow, many of us seem to put ourselves in this position unfortunately. I, for one, never ever thought that I would be living like that. I am very strong, and very feminist. But also extremely capable, and this may be half the problem. My DH really didn't see the disparity. Now, he agrees that how it was for a long time was not OK, with hindsight. But I don't think he fully understands how much it hurt me (or how close I was to leaving).
I think one of the issues may be that when kids are small and both parents work, time is deeply scarce for both partners and the one not pulling their weight properly is still knackered. I think that, in that situation, sometimes its hard for one partner to fully realise that their time in front of the TV/ doing sport etc which they feel they really really need, is 'robbing' the other partner of their equivalent time. Also, when you are both tired, a dynamic sets in where you are both 'competing' for that scarce resource.
What I basically learned was that, in that context, arguments about the overall parity of work don't work. Change happens incrementally.
Pick the first battle (washing/food shopping etc.), sort it out and then move on to the next thing.
I hope it improves for you.