I know that you can use a digital multi-meter to measure a headphone's impedance from the sleeve to the tip or ring on a TRS or TRRS jack, but I don't know what frequency it's being measured at. If I wanted to do a full-frequency impedance plot for something like a custom in-ear monitor or a multiple-driver balanced armature, how would I go about doing that?

Technically, you need a source with a known (and preferably purely resistive) output impedance, and measure its frequency response with and without the headphone load, then the impedance can be calculated from how the frequency response (including the phase response) changes. There are various software packages like ARTA that can do this, some may be available for free, or as a trial version. Also, the utilities linked in my signature can be used for impedance measurements, but they need to be run from the command line, so you might not find them very user friendly ('testgen' creates a test file in WAV format from the included imptest.txt, 'impedance' analyzes the loopback recording, and 'fft' creates the graph as a .bmp file).