Go to the Bluetooth page in Settings. Tap the gear to the right of the headset and see if the box next to Phone is checked. If not, tap it to check it. (If it doesn't "stick", do it the next time - it may take 2 or 3 times to get it to stay checked.)
I have the opposite problem. When I make or receive a call the do not disturb icon appears and I cannot hear anything. However, if I'm in the car the phone works fine with the built in Bluetooth. I hope someone has a solution as I'm fed up with having to start the car up every time I need to make or receive a call.