I think every couple since time began has had issues with the same things. One of which is household chores. And sadly I do not think anyone has come up with a good solution yet.

I've heard of a few different things couples do....
1 - The one home 1st cooks, the other cleans up afterward, alternate weeks of doing the bathrooms and vacuming, one goes shopping this week, the other goes next week and so on.
2 - Use days off and do everything together splitting everything in half.
3 - Even numbered days your turn, odd numbered his.

In the end I really don't know if any of that works.
Good luck.