OK, I solved this one on my own.
I'm running the PilotEdge plugin. (Live, professional ATC. IMO, it's awesome.) Even though I wasn't connected to PilotEdge, some how it's presence is why I wasn't visible. The way I figured that out: I installed PE on the other computer (just trying to eliminate variables) and as soon as I did that, his aircraft disappeared.
If you're a PilotEdge user and you have this problem, you can just move the PilotEdge folder out of resources\plugins (I just stuck it on the desktop) when you want to do multiplayer. Then copy it back in when you want to fly with PE. I'm not sure what would happen if we were both running PE and connected to the PilotEdge system. Presumably, then we would both show up. I may sign him up for a free account and see what happens.