Most bluetooth headphones can't handle stereo sound, plus using the mic. You would have to go into windows sound and switch speakers to hands-free audio for your bluetooth headphones. In my personal experience though, your bluetooth headphones will start buffering audio, and if you stop playing audio, the bluetooth will continue playing audio from the buffer for a few minutes depending on the size of your bluetooth memory buffer. That also means audio sync will probably be lacking as well.
Apparently, there are some bluetooth that can handle stereo while using the mic, but they cost more, they use proprietary technology.
If you want to use the stereo of your bluetooth, then don't use the built in mic, use a 3rd party mic instead.