I grew up in a multi-generational house (me'n my sibs, parents, maternal grandparents) that my mom grew up in multigenerationally, and her dad grew up in multigenerationally, and his mom grew up in multigenerationally, and that her parents or grandparents (forget which) built.
In a couple of years our family will move back there to do the same---me, my husband, our kid(s), my parents, and maybe still my grandfather.
It's a big old farmhouse and it's actually built almost like a duplex with a central hall/staircase and then, on either side of that, a separate living/kitchen/dining area for each generation (counting the young family as a unit).
Upstairs each side has its own bathroom and three bedrooms. The washer/dryer is shared.
If my grandfather has passed by the time we move back things will be simple as far as living space (our family will take over his half of the house); if not, it will be a bit more complex. I will be his primary caregiver if he needs care. He'll probably keep his downstairs and we'll take his upstairs, sharing my parents' living/dining space.
I don't have any insight into this from the parenting perspective, but as a young child it was pretty great. My grandparents never visibly interfered with my parents' parenting, but were available for childcare backup. We lived parallel lives; when gramma was living she fixed all the meals for her and grampa, and they ate together on their side of the house except for holidays or other special occasions (birthdays, etc) when we'd all gather in the biggest living space available. After gramma died, my mom invited her dad to come share meals with us, but he likes his own space and to watch TV while he eats, so now she cooks and carries the tray over.
Unsure exactly how finances were managed. There's no mortgage on the house, obviously, and it's in my grampa's name (will be in my mom's after he passes). I imagine everyone chipped in for taxes and utilities. I think now, because my parents do all the cooking, they also pay for all the food, but possibly grampa pays for all the utilities. Dunno.
My parents and husband and I have discussed at some length how we might work it when we move back (need to finish remodelling and sell our current house). I think we'll just split fixed expenses among all available incomes. My husband will be the stay at home parent; he's also a carpenter and this 1850's house needs EXTENSIVE work so that will be his big contribution besides childcare. Both my parents are still working and I probably will be too. I think I'd like to do more meal sharing.
BUT I am really really interested to see how this works for others! Is there anyone else, like me, planning to live with extended family as a permanent arrangement rather than a temporary one? (Not like I'm not excited to hear from the temporary folks too, 'cause I am!)