I've got a Windows Mobile 6.1 Standard phone and a Bluetooth headset that only supports the Hands Free profile. When I partner up the phone and the headset, phone calls come in just fine through the headset, but I cannot listen to anything that is
playing on Windows Media Player. However, I have installed some bluetooth software on the phone that allows me to listen to music or podcasts that are playing on Windows Media Player.
So the answer to your question is that it is possible to also listen to music through a bluetooth headset (that only supports the Hands Free profile), but you'll probably need to purchase some software before you'll be able to do it. I haven't used
this particular application or
this application but you might want to give it a try and see if it makes a difference.