Actually, I see the problem: One of us is talking about broad categories that you might watch for in an artist call or enter on an application, and the other may be thinking mostly about descriptive text that could go on a title card next to a work in a gallery. In the latter case a viewer could easily see that something was a painting, or whatever, and would appreciate any available detail. In the former, someone reading a printed application probably couldn’t readily see the work at all, and might never need to — while the juror for the show would be scrutinizing the work but would probably (in my experience, at least) never see the application. No doubt, though: the word “medium” is widely misused.

That makes sense, Alyson, by the dictionary definition of “medium,” and it might work — with painters, instead of putting down “painting” when an application asks for medium, saying, “oil” or “watercolor” or “mixed mediums,” and sculptors saying “marble” or “clay,” or “mixed mediums,” but in practice artist calls often list mediums (or “media”) as the old familiar painting, sculpture, fiber arts, film, etc, and I think it’s too late to change the word that they use. And when a particular show says that the only mediums that it accepts are painting and sculpture, a painter shouldn’t give up because they didn’t list oils or watercolor.
I think we’re stuck with the misuse of the word, but l kinda like the idea of someone, when asked what sort of work they’re entering in a show, saying “Brazilian Rosewood.”

Neither Sculpture nor Assemblage is a medium. They’re both categories of art – like Painting, Photography, Fiber.
A medium is something you use to make the assemblage or sculpture.
A sculpture would be bronze, marble, aluminum, wood (the more specific the type of wood, the better), etc.
So, to answer your question, Arthur, you wouldn’t even put “assemblage” in the medium. We can see that it’s assemblage. You would just list the components you used.

Maybe so, but following that logic I’d have to say “Sculpture” when they ask for medium, which would get us farther away from useful details, not closer. So I guess it’s preferable to say, “Assemblage: blitz, blotz, blatz.” Some places really want to know, and it probably won’t bother the rest. Unless there’s one tiny field on the application that won’t hold more than one word . . .

I think the best answer is to talk to the venue in which you are showing, but otherwise, it is best to keep your own system of notation that is clear to you. I have seen both, but assemblage is not really a medium it is a technique (technically).