As a matter of fact, iMovie can not support the direct import of AVCHD (.mts) files form HD camcorder, and even the latest version iMovie 11 still does not support the import of AVCHD (.mts) files from a number of camcorders.
So maybe there is need for you to convert your sony hdrcx115e mts videos to aic mov with a mac mts converter program at first. Below are the simple steps.
At first, connect your hdrcx115e camcorder to Apple computer via USB cable, find the .mts files by following the camera folder AVCHD > BDMV > STREAM. Then copy and transfer the .mts files from camera to the Apple hard drive disk.
And then use a mts converter mac program to convert your sony hdrcx115e mts videos to aic mov for further editing. Maybe this program could do you a favour: Brorsoft MTS/M2TS Converter for Mac.
It's able to convert 1080p/1080i/720p AVCHD/AVCHD Lite footage(*.mts, *.m2ts) to Apple ProRes, Apple Intermediate Code(AIC), Avid DNxHD for further editing with FCP, FCE, iMovie, Avid.
I suggest you convert your cx115e mts to aic mov with 1920*1080 video resolution for further editing with imovie.
After the video conversion, you will be able to get the output files for iMovie via clicking on “Open” button effortlessly.