I've noticed that the latest versions of iMovie only recognize DV video with 16-bit audio recorded. Note that many miniDV camcorders offered the option to record in 12-bit audio, so you could add a "voiceover" track later (in wonderful 4-bit audio.)
I did some testing, and on my Sony and Canon miniDV camcorders, neither one will import to iMovie 10 properly in 12-bit audio mode. Some won't have audio at all, some will do as you see, apparently work, but not export properly. If your JVC deck has an option to convert all audio to 16-bit, use that.