From what I've read elsewhere, this functionality is generally handled by the application playing the music/audio. So, I've been testing out various players, and found a couple that do what Casey is requesting, MX Player and Poweramp.
MX Player is primarily known as a video player, but it can also handle a number of audio formats (including Opus, which I happened to be looking for).
One drawback with MX Player is that it can't create dynamic playlists, so you have to have the songs ordered in folders to play in succession.
The other one that does what Casey is requesting is the music player app Poweramp, which lets you choose in its settings, under Audio->Audio Focus->Short Audio Focus Change, between no ducking (unchecked), and pausing (checked). Poweramp isn't free, though.
Another app, Rocket Player, is a music player that will let you choose between ducking and pausing, but will not allow you to disable it completely, which is what Casey is looking for. (The setting is under Settings->Sound->Audio Focus->Temp Focus Action)
For myself, I've found that, especially for audio books and podcasts, I actually prefer pausing to ducking or no ducking, so I like Poweramp or Rocket Player for this purpose.