My X is connected to my car using the Headset/Handfree profile. This is how I make/take calls, open the phone book, etc. Then I use a Blackberry Bluetooth Stereo Gateway (plugged into my car's AUX port) and the Bluetooth A2DP profile for Music from my X. This allows me to not have to have a wire from the headphone jack on the X to my car's AUX port, and listen to music via Rhapsody, or songs stored on my X.
When streaming music on the X (using Rhapsody or its internal music app) via Bluetooth & the BB Gateway, I have the car stereo on AUX and I hear all the assist sounds. I hear Google Maps navigating. etc. I can have it read me the texts, notifications, etc across the car stereo's speakers. And I am able to interact with the X.
However, when the car stereo is set to Radio or CD, the sounds of the X are still being sent via A2DP to the BB Gateway, and I wont hear them because the car is set for the "other source." Thankfully I can drop the connection to the BB Gateway, and still have the X connected as Headset/Hands free. This allows me to hear the sounds, notifications, etc via the X's speaker yet still make/take calls via the car's bluetooth setup.
I would imagine your car does the same, except that the bluetooth receiver in your car stereo supports both Headset/Handsfree and A2DP.
When I use the X with my Moto S11 Flex HD stereo headset, the X connects to it using both headset/hands free and A2DP. While listening to music, I still hear the Assist sound, notifications, and can interact. The music pauses or fades out while the phone plays the notification.
When using the S11, under the X's bluetooth options for it, I can DISCONNECT the A2DP or MultiMedia Audio profile and still have the Headset/Hands Free connected. This allows me the use the S11 only for phone calls, like a traditional BT headset/ear bud. And assist sounds/notifications/etc to come out the X's speaker. This might be what you need to do.