"This is a very interesting apartment building."
Translation:C'est un immeuble très intéressant.
Immeuble is as imprecise as it gets. It literally means something that can't be moved. It can commonly refer to an apartment building, an office tower. It can also technically (= lawfully) refer to a house, a tree...
The English on the other hand is very specific apartment building = a building containing apartments. We don't have such a precise term. If you want to be precise about it you could say un immeuble d'habitation, but it's not common at all.
"Apartment building" is fairly general English, and used in many places besides the US. In contrast,"block of flats" is pretty British. And while US city blocks are often larger than in European cities, "block" still IMO usually means multiple buildings within a single area enclosed by roads, not just a single building, unless those two definitions overlap in that specific case.