Few ways I could think of doing this
1) Frames. Yuck I know, they are not 100% search friendly. But with some .htaccess trickery you could manipulate the frame to show up regardless of the page called.
Thinking behind it..
If a page is loaded not inside a Frame.. redirect to a PHP page that dynamically rebuilds the frames with 1 frame the MP3 player and the other the page desired. This needs severe testing testing because what if you accidentally load the frame page within the frame page????
2) Pop up Window. Pretty self explanatory.. of course you run into the possibility of the user disabling pop ups. Which leads to the VERY user friendly option of “Click Here To Listen To Us”. It loads a pop up, a user knows about it, where it is.. and can keep it open.
3) Redesign WordPress to be 100% ajax!
-Tesh