Huh. Strange. I think you're both picking nits here. If you "raise" a regular surface street so that it passes over something, a railroad grade, highway, etc. It is an overpass as far as that road(the one being raised) is concerned. However, it will be an underpass for the surface feature that is now passing under the raised roadway. The definitions, you'll find will vary wildly from area to area.
California DOT for example, seems to decide Over/Underpass status depending on where the "most significant" roadway grade currently is(not to be confused with where it may have been in the past), and what the initial grade was has little evident bearing on the naming used unless you're dealing with "Equally ranked" highways(such as two Interstate highways). So in California, if you have Maple Street passing under an elevated Interstate 5 for example, it would be the "Maple Street Underpass" so far as California DOT is concerned because it passes under Interstate 5, even though it was Interstate 5 that was obviously raised above its original road grade to grade separate them. If Maple Street instead goes over Interstate 5, then it obviously becomes an Overpass as it goes over Interstate 5. (Of course, to be fair to CalTrans, they actually label them as being UC or OC respectively, so I'd presume UC=Under Carriage and OC = Over Carriage, so they technically aren't even using Underpass/Overpass, but they are expressing the same sentiment)
Personally, I'd be inclined to say over/underpass status depends on which road remains closest to the original roadway grading, and where the other road crosses it(going over or under), but I think you're going to be hard pressed to find that standard, or any other, rigorously applied just about anywhere.