On a technicality slaves would make it “multi-family”, but good luck trying to explain that to them haha. Thats a far better explanation though and would fit the era I would assume.
Middle class is a sometimes-nebulous term. In this context, think less "an independent blacksmith" and more "a merchant who isn't particularly wealthy"
Might be wrong but I think the middle class would have been proportionally a lot smaller percentage of the population than it is in modern Western societies.