Both my babies were criers. Big time. DS2 always wanted to be held. So I couldn't have managed in your situation if DH had refused to do anything around the house. The way we worked it was that we both agreed that my main job when I was at home and he was at work was seeing to the kids' needs i.e. feeding (bottles/breast/meal preparation when on solids), getting to sleep (this takes a LONG time sometimes with a colicky young baby, with frequent interruptions and resettling!), making up and washing bottles, cuddles, playing, taking out for walks, cleaning up day-to-day mess in kitchen, trips to baby groups, tidying up after baby etc
All the above can seem to take all day, I know. When my two used to have their main nap at lunchtime, that was the time I had my lunch, washed and made up bottles, cleaned up the kitchen and sat down with a cup of tea for half an hour. When they were awake they were very demanding so no time to do big jobs like cleaning the bathroom or doing a mound of ironing. So things like that I used to leave till the weekend and I would do them then while DH was in charge of the baby.
But ordinarily during the week it was what I described PLUS I could manage to also fit in a big food shop to the supermarket, putting the washing on every day and hanging out to try and folding into piles for ironing at the weekend, errands to local retail park for things like birthday presents etc. (difficult if transport an issue, I know).
There is little time to do anything else really during the daytime if you have a demanding baby. For me, big jobs such as cleaning the bathroom and major tidying and even hoovering got left till the weekend. During the evenings, one would bath the baby while the other one did a quick tidy and prep of our evening meal. Then someone would put the baby to bed while the other one actually COOKED the tea, which we'd eat once the baby was asleep. Then we would BOTH clean up and finally BOTH sit down for a bit of relaxing time. I would always be the one to go and resettle the baby, though, and always the one to get up in the night with them. Fair enough I think.
Sorry, this is really waffly but I just wanted to show you what worked for us. You just can't possibly do ALL of it. Your MAIN job is caring for your baby - you wouldn't pay a childminder money to look after your baby then be happy for her to spend hours doing housework while your baby was in her care, so why would your DH be happy for you to do that during the day?