We have a loving, healthy relationship. We drink in the same room, sometimes even at the same time. 
This is going to sound really nauseating, but our only long-running conflict (we don’t even argue about it, which sounds even more nauseating) is that we each think we don’t do enough. He works full-time, makes almost all the money, deals with the bills and retirement accounts and stuff, keeps the garden watered and pesticided, and does about half to three-quarters of the cooking. I work about 15 hours a week outside our property, take care of the house and most of the laundry, mow the yard, dig and weed the garden, cook most of the time he doesn’t, and deal with all the animal-related stuff.
But if he actually sees me picking up after him, he gets upset because he says it makes him feel useless not to contribute. I think he’s nuts, because, c’mon, look at all the shit he does. He contributes plenty. And if the house isn’t pretty clean, or the yard/garden doesn’t get dealt with, or the litter boxes aren’t scooped, or my paycheck isn’t enough to cover whatever I feel like I ought to be paying for…I feel like a useless slug. He thinks I’m nuts, for pretty much the same reason.
I feel sort of stupid even mentioning it, really, because it’s such a great problem to have and I know full well how many people have the exact opposite problem of not having nearly enough respect for each other’s contributions. And near as I can tell, the only real solution is for us to each get over ourselves. I will say, though, that I feel like I’ve made a lot of progress in the self-getting-over since I first made the transition from working full-time to our current situation. I dunno about him.
We have a good system that seems to work.
I take care of:
Cooking
Cleaning
Grocery shopping
Laundry
Making beds
Garden
Car washing and gassing
Bill paying
Finance
Picking up
Putting away
My wife takes care of:
Deciding which TV shows we will watch
Deciding which movies we will see
Deciding what music we will listen to
Shopping
Pointing out where I am wrong
Scolding me when I ask her to do something
So, it’s pretty even. At least there is the lack of sex to make up for where it isn’t even. 
My partner and I have slightly different parenting styles. As a result, we were getting into arguments and inadvertently undermining each other. So we came up with this plan: one person is In Charge of our son at a given time. Generally, my partner does the morning routine and I do the evening. On the weekends, we just decide who is In Charge at a given time. Whoever is In Charge parents as she sees fit – and the other person has to back her up. For example, our son fusses for a while at nap time. The person In Charge determines how long and to what degree he fusses, and goes to check on him if necessary. The other person does not go in to check on him, unless specifically asked. Our rules aren’t that different – it’s more a matter of nuance and timing – which I don’t think will horribly confuse our son.
Whoever is In Charge has to keep an eye on our son, while the other person can move about the house at will, do housework, talk on the phone, chat with company, or whatever, without having to multitask with watching the kid. It really helps to get a break that way! Of course, if the kid was about to swan dive off the stairs, I would stop him, whether or not I was In Charge or not. But with other things, I defer to my partner when she’s In Charge.
I wish I had a solution for this one: the kitchen sponge. I try explaining why we need to rinse and squeeze out the sponge but to no avail. I keep finding waterlogged sponges in the sink with food stuck to them. Why, I ask her, are they hunting for water on Mars? Because life needs water to grow! A dry sponge does not encourage as much bacterial growth as a warm, wet one. To no avail. I do stick them in the dishwasher and/or throw them out frequently to keep from poisioning all of us. But I really wish we could get a little more use out of them.
Another solution is to get a maid to come in now and then and you will both still feel like you don’t do your share, but you’ll know why, it’s to give the maid something to do. (Ha ha)
Reminds me of the flap my daughter creates when she comes over. She likes to use the kitchen hand towel for mopping up spills, to avoid wasting paper towels.
I use paper towels for spills and the kitchen hand towel for drying my hands.
So sometimes I dry my hands and find them smeared with ketchup or something.
My solution was to put out two towels with little smiley face post-its on them. One a girl smiley and one a daddy smiley.
I don’t own a sponge. Got a dish brush and whenever the dishwasher is run it’s in the top rack so it’s always as clean as the dishes, no chance to get moldy.