Possible fix
Open messaging
Go to settings (menu button)
Under notification settings, select ringtone and make it SILENT
I selected vibrate to make sure I knew when a notification came through though. I am using Android 2.0 (Moto DROID) and I don't think it makes a difference but I have the Rings Extended App installed. I say that just in case doing this without the app installed does not work for you, that might be the quirky reason why.
You would also have to do this for all the GMAIL app i found out because it will interrupt your music.
My hunch is that when you put the phone's ringer volume on vibrate or silent, the music/ringtone that plays for your notification still plays when they come through only it inaudible since you put it on silent. Therefore the "silent interruption" you get while listening to your music is your ringtone playing...but you can't actually hear it.
HTC folks, please post and let everyone know if this works on your phone so other's know since I'm using moto DROID.