I think if you're filling up a garbage can every day, you need to check what you're eating. Sounds like WAY too much pre-packaged food.
Regardless of that point, at Casa DzlBenz, there is no such "my job/your job" division per se, however there are some specialized tasks that are specific to each of us. I mow the lawn, keep up the cars, maintain the house structure and mechanical systems, and so on, because I enjoy doing those things. Mrs. Benz does the sewing, gardening, decorating, most of the cooking, all of the baking, shops for the kids' clothes and so on, because she enjoys doing those things. All else is up for grabs. My masculinity is not threatened in the least by washing dishes or running a vacuum. Her femininity is not threatened in the least by taking out the trash or putting sealer on the deck.
In our household, the everyday tasks are addressed on an as-needed basis. If the trash needs to be taken out, the one who notices does it. If the kid is wearing a shitty diaper, he who smells it, well, deals with it. (Just doesn't quite work in the present sense, does it?) Fortunately, that issue is going away as #2 Benz-ette has turned the corner on potty-training, at long last.
A marriage and raising a family require an equal committment from all involved to do what they can to help the lives of the others. Running a household requires mature adults to recognize that there are things to be done, and you'd better be a big enough person to not let your pride get in the way of taking out the damn trash or folding a shirt.