Apple claims that iMovie '09/11 supports most commonly-used video codecs, including DV, MPEG-2, MPEG-4, H.264, AVCHD and AIC. However, due to the wide range of media types, and the different ways manufacturers store video on these media types, not all AVCHD camcorders are compatible with iMovie '09/11. In this case, the workaround for you is using a Mac AVCHD Converter to convert/transcode AVCHD MTS files to AIC for iMovie.

About Apple Intermediate Codec (Quoted from Wikipedia)
“The Apple Intermediate Codec is a video codec designed by Apple, Inc to be an intermediate format in an HDV workflow. It features high performance and quality, being less processor intensive to work with than other editing formats. Unlike native MPEG-2 based HDV - and similar to the standard-definition DV codec - AIC does not use temporal compression, enabling every frame to be decoded immediately without decoding other frames. As a result of this, AIC takes three to four times more space than HDV.
AIC is available only on the Mac OS X platform and cannot be read on other platforms to date such as Windows or Linux. All Mac OS X software which makes use of the QuickTime codec libraries - primarily Final Cut Studio, Final Cut Express, and iMovie, but also freeware such as MPEG Streamclip - can use the Apple Intermediate codec.”
What you will need?
Mac AVCHD Converter
Guide on how to convert/transcode AVCHD MTS files to AIC for iMovie
Step 1: Free download Mac AVCHD Converter, install and run it.
Once run the program, you can click “Add” button to load AVCHD MTS files. The Mac MTS converter supports batch conversion, so you are allowed to add multiple files to convert at a time. Meanwhile, if you wanna combine multiple files into a single AIC encoded .mov file, you can put a checkmark in the checkbox “Merge into one file”.

Step 2: Select Apple Intermediate Codec (AIC) (*.mov) as output format for iMovie
In order to convert AVCHD to AIC for iMovie, you just need select AIC (*.mov) as output format for iMovie. Please click on the dropdown menu of “Format”, and then follow “QuickTime Movie Format” > “Apple InterMediate Codec (AIC) (*.mov)”.

By the way, the Mac AVCHD Converter also supports output Apple ProRes format for using in Final Cut Pro, you can visit how to convert AVCHD footage to Apple ProRes 422 encoded files for Final Cut Pro to learn more.
Step 3: Adjust audio and video settings
The Mac MTS converter enables users to adjust audio and video settings before transcoding MTS to iMovie AIC. Click “Settings” button, then you will enter the following interface, on which you are allowed to customize size, bit rate, frame rate, sample rate, and audio channel to your required ones.

Step 4: Convert/transcode AVCHD MTS files to AIC
Click “Convert” button to start transcoding MTS to iMovie AIC. With perfect audio and video synchronization technology, the Mac AVCHD Converter will never cause you any audio and video out of sync issues, which is much better than other similar tools in the market. When the conversion is finished, you can click “Open” button to get the final output AIC MOV files with ease.




