To provide a little more illumination on how the SDHC conversion works in Final Cut Express;
When you either mount the camera in disk mode (or have the SDHC card inserted in a card reader) and open the Log and Transfer window, the name of the volume appears with a spinning progress indicator:
After about 20 seconds, a list of clips appears. You can preview them, set in and out points, or simply drag from the top window to the bottom. The bottom window is a queue of clips to be converted.
Note that FCE only seems to recognize AVCHD files if they are contained within a valid file structure. If you try and copy the .MTS file into Log and Transfer from another location, you get an error message: