Step one, when you copy the files from your camera, don't just copy the .mts files. Copy the entire AVCHD folder. This folder contains other data/info. (a directory structure for AVCHD files) Bring that whole folder off of your camera, and place it somewhere on your computer's harddrive.
Step two, go into CS4's media browser window and navigate to the "AVCHD" folder that you brought from your camera. Click on that folder and it will automatically see the .mts files as one large "stitched together file" just the same as your camera does when you playback the footage from the camera. (no more audio or video frames dropped at the joining of clips) From the media browser window, import the footage, then take that footage from your project panel to the timeline.
Note: AVCHD footage is HIGHLY compressed.....if you don't have MAJOR horsepower, you will find it difficult or next to impossible to edit/playback native long-duration AVCHD clips on your timeline. The next thing to do then is once you have taken the file from the media browser to the proj. panel, and then finally to the timeline, export the timeline to the Adobe Media encoder, and transcode that file into a format that is more edit friendly. (Mac users can transcode to Prores....which is FANTASTIC. PC users will have to use uncompressed AVI, or download the Cineform codec.)
This takes a few hours, so set it up to transcode before going to bed at night, and your editable files will be done when you wake up.
Hope this helps.
Sorry to hear that didn't work for ya. I have edited AVCHD in CS4, on a buddy of mine's CS5, and also in FCP and I have yet to have trouble with any of them recognizing the files as large stitched together files.
If you find out what is causing the trouble...be sure to post it up here for all of us.