Does anyone else use the term "flat" in the US to refer to a unit of a duplex, where the duplex is by floor (1 unit upstairs, 1 unit downstairs) rather than side by side?

I lived in a building like that in a Midwestern city. Central stairs divided each floor, one apartment on either side. 4 story brick building. We had 3 full bedrooms, a large living room and a dining room. There was a small bedroom off the kitchen, probably once meant for the cook or maid. We stuffed 4 or 5 folks in it, college-aged and into our 20s. The couple sharing a room got the one with the toilet & shower attached. The student with the least money took the maid's quarters, and a corresponding discount on the rent. My understanding is that these multilevel brownstones were originally rented to middle-class families (Husband & wife, a kid or two and a servant) in the late 19th century. Possibly modelled on British mansion flats, like Horace Rumpole lived in. Ours was near the lakeshore and the local state U. It was a 45 min bus ride from my job, until I switched employers to one downtown. Then I didn't need a car, as I could walk, take the bus or ride my bike 3 mi. There was shopping in easy walking distance, along with an entertainment district.