Talk about it, in detail. Talk about what needs to get done, and how often it should get done (you two may have differing opinions on this). Then divide it all up - if there are things you hate doing but he doesn't mind, he gets those, and vice versa what what he hates doing. Then the other stuff gets divided equally by the time it takes. Idea is that you each end up with a roughly equal time commitment to get your share done.

You could decide to switch it off by week or month or whatever, so nobody's stuck with the same chores forever.

I agree with you that you shouldn't be "in charge' and have to tell him to do things. But I'm guessing from your description that his opinion on how often things need to get done differs from yours, so you get to the point where you think it needs doing before he does. Y'all just need to talk about it and come up with a plan than works for you both, which seems fair and equal.