I want to describe my average day/week, because I suspect that our days are more alike than different and that we simply think about/define them differently.
Here's what we do: We all get up at about the same time and my partner and I both keep an eye on the kiddo until he leaves for work. Most days Daddy gives Jackson breakfast because Mama has not had enough coffee yet to be human.
During the day I usually do some laundry and wash the morning dishes, plus tidying up whatever disasters the little guy creates as he explores the house. Once or twice a week I manage to do something else, like clean the bathroom or vacuum during the day. During the week we run some errands like grocery shopping as well as going to a couple of playgroups, the library, the park, the gym...
When my partner gets home from work, he plays with the baby for 30-60 minutes, depending upon how hungry we are. I sometimes use this time to get some chores done but more often I veg out on the couch watching them play. Then, my partner cooks (almost every night!). Lucky for me, he loves to cook and he's really good at it and he likes cooking as a transition to being home. While he cooks Jackson and I play, sometimes we 'play' at doing laundry, and our w/d is in the kitchen so we're all together. After my partner gives Jackson a bath while I do the dishes. While I'm nursing the baby to sleep my partner will sometimes tidy up something, sometimes work on balancing the checkbook or paying bills, sometimes he will get a beer and watch tv.
On the weekends, we negotiate. We sit down for a minute and talk about what needs to be done, what we can do together, what we'll need to trade off hanging with the baby in order to get done. We make sure that most of our weekends include time together as a family as well as a break for me (usually a couple hours on Saturdays when they go out and run errands or do something fun).
Our house is not immaculate, but it's tidy and clean. This is what sharing responsibility for housework looks like for us, and it works pretty well most of the time and neither of us feels taken advantage of or resentful.