Not normal.
My husband and I are both geologists with similar levels of experience. We both worked in various sectors, important for the story because some sectors expect the world and beat the hell out of you. We have traveled a lot so there have been times when he’s staying at home taking care of pets, and vice versa. He had the life experience of being in the American military as infantry for eight years before we met. Now we are both working and share the duties.
When he was staying at home, life hadn’t kicked me in the teeth yet, so I wasn’t as kind as I should have been. Overall I was understanding because I could see he wasn’t sitting on his laurels all day but I would want a deeper clean than he would do on things. I sound a bit like your husband, though I never ever threatened not to buy him something because it’s not my money it’s our money and he’s a grown man who can do what he wants and I trust him not to buy things we can’t afford when times are tight.
When I was stay at home, he couldn’t have been kinder to me. He’d chip in by doing whatever needed to get done if I hadn’t gotten to it yet. If I didn’t have a plan for dinner because I didn’t get the grocery list finished yet, he’d make something simple or just pick something cheap up for us on the way home from the cheap menu at fast food places. If it didn’t need to get done and it wasn’t done yet, he didn’t sweat it and he would let me get to it the next day because he knew I saw getting this crap done as my contribution. He never gave me a list of things to do each day. Sometimes if I’m not remembering things I would ask him if there was anything that he wanted me to do, most of the time he’d say something like “you’ve been working so hard take a day to yourself”.
I credit my husband’s maturity and the fact that he’s seen the world and life kicked his ass in the military with his incredible understanding and kind nature. And if anyone wants to try to tell either of us it’s because he’s “sensitive” or something like that, he tested expert in the rifle and the pistol as soon as he got to boot camp, and only got better with training. I wasn’t as kind until life kicked my ass. Maybe your husband needs life to kick his ass or walk a mile in your shoes to understand.
Last point- his examples suck. You not putting dishes away that are in the drying rack as “not completing” the task is not comparable to paying the bills. It’s more like does your husband complete every single task he’s assigned to do at work every day? Or does he work on tasks where as he leaves work all of the tasks he set out to do that day are all tidy and complete and QC’ed for completeness? The latter type of job doesn’t really exist outside being a server, bartender, cashier, those types of jobs.