If you're a stay at home parent, do you do everything?

I'm a first time mom and a stay at home mom. (This is both my and my husband's choice and we are fortunate that we can swing it, no judgment to working parents out there, I think all parents are amazing!).

My question to those who are stay at home parents: do you do everything? My husband works a full time job and I take care of the baby in basically every way, as well as the housework, budget, errands, and other general daily stuff. When I say I take care of the baby, I mean in every way. My husband has never once bathed her, trimmed her nails, read to her. I change diapers, I get up with her at night, play with her, read to her, sing to her, put her to bed. I don't mind this because I don't work outside the home and I appreciate my husband for providing for us. Though he does get very annoyed with me when I ask him to watch the baby so I can shower or go to the bathroom alone. He'll do it, but he rolls his eyes and sighs dramatically and says FINE (and occasionally "you know I work all day!"). He spends at least an hour, usually more per day decompressing by playing video games. He takes a minimum 45 minute shower at least once a day (often twice on weekends). My showers are usually 5-10 minutes.

It makes me feel guilty for asking to take a shower and it makes me sad. Am I out of line? I feel like I would like to decompress too sometimes but I just don't get the opportunity, especially without guilt. I know how lucky I am to be able to stay home with my baby and I wouldn't change that for the world but I am so tired and so rarely get a break. I'm just curious what other people's dynamics are who have one parent who works and one who stays at home.

Thanks, friends!