Seems to me this is a BT Profiles thing, the Rezound will only play music (media) over BT to devices that support the Advanced Audio Distribution Profile (A2DP), and the Jawbone II only supports Hands-Free Profile (HFP) and HeadSet profile (HSP).
Yeah, but most newer BT headsets support the A2DP profile, for about $30 on Amazon or eBay you could get a suitable replacement, in fact, you can even get a nice stereo headset (I recommend the Kinivo BTH220 or iKross 1KBT18 if on a budget) for less than that from Amazon.