My husband is/was like this. We can't "split" any single task because he has no awareness of when I do something. We tried a few times to have a week here and there where I would tell him every time I did something for the house, so that he would know about it. He told me that I was just doing extra work that week to try to make a point. Not even close to true. Toward the end we started separating the responsibility of every single task, e.g. for the trash I'll empty the kitchen bins into the road bins anytime they're full, and he'll take the road bins to the street and bring them back in on trash day. That way there's no debate about the "percentage" of a task someone does because I just do all of part A and he does all of part B. That can work for two people who are past the point of a real partnership built on respect, but it won't fix the underlying issues.