This won't solve your problem permanently but it will show you how to work around it with a minimum of trouble. This works for me every time.
As far as I can see, the phone/audio conflict happens when the phone is already connected by USB and then subsequently connects by bluetooth. To make it work, the phone has to connect by bluetooth first and then subsequently by USB. So here's the procedure.
1. Start the car with the phone unplugged.
2. As soon as you see the little bluetooth light come on, showing that the phone is connected, you can go to the next step. Hit the voice button and say "USB." It will say something like, "No device found," and switch to Line In.
3. Plug in the USB plug on the phone.
4. Say the "USB" command again. This time it will work. From then on, for the rest of your trip, you can switch between audio inputs, take phone calls, etc., and it will still work.
In general, just make sure the car is on, the bluetooth is connected, and the car knows no USB device is present before the first time you plug in the phone. If you do this wrong, you'll see the iPhone but get no audio. No need to switch off your car or anything like that; just go around again. If you're already set to USB and it's not playing right, just unplug, wait a second, re-plug, and switch back to USB.
I'm driving a 2011 Ford Escape with Sync.
--Joe Pride