I am married to a man who works only part-time (from home, very brief hours) and who may very well discontinue even part-time work if I get another promotion/better job in the next few years.
Let me describe to you a little bit of how he does things -- the kinds of arrangements that had to be made in order for me to feel comfortable being the sole working parent.
My husband does the night wakings with our baby 6 days out of every 7 (Saturdays, he gets a lie-in while I handle the waking, and some Wednesdays we go to his parents' house and they do the night wakes). He gets up before me to play with the baby on the baby's ridiculously early schedule, drives me to and from the transit station daily (it's too long to walk, we're in the US).
While I'm at work, he tackles 3-4 cleaning tasks a day. We mostly are able to keep on top of housework, though we have someone come in twice a month to do a little more of the "deep cleaning" that can get neglected in a house where everyone's always running after a newly-crawling baby!
When I get home, I like to cook dinner (cooking's always been one of my strong points!), so to make it easier, he usually unless it's been a crazy day with the baby, which is fine and happens once a week or so gets out everything I will need to make dinner, so that it's ready to prepare. Sometimes he'll even do some of the chopping/prep work so I don't have to.
He does 90%+ of the baby's diapers, feeds him breakfast and lunch (dinner is my special baby-and-me time), takes him to appointments, does the dinner cleanup while talking to the baby about what he's doing, and so on. When the baby is a few years older, there'll likely be a sibling or two following, and we intend to homeschool at least during the elementary school years.
In a few years, we hope he won't have to do any paid work at all to supplement our income. But in spite of the non-paid nature of his work, he works HARD in our home. He has spent the last year getting better and better at housework and logistics as I went through the final stages of pregnancy and we started adjusting to life as parents. He's a total whiz at childcare and spends so much time with our little boy ... and it shows, in their deep, loving bond.
If the stuff I'm talking about here isn't something your husband would be willing to do, he's not a househusband or a SAHD, he's a cocklodger who you aren't even having sex with.