IDK what you have. (model), On my SE (not JBL), I simply paired it. It works fine for both streaming and phone. Primitive but it works

 

Check your owners manual for your particular model year / headunit and follow those steps, you should be able to get both working at same time. On my 2012 Ltd, I have to do the phone setup first and during that process it asks if I want to use the bluetooth audio player as well - answer yes and continue setup. If you setup the bluetooth audio player first, then the phone function didn't work.

 

Very strange. It started working yesterday. Perhaps it was turning the car off and turning it on again.

 

Noticed today while driving it only paired with the handsfree not the audio. Seems the pairing mechanism is unreliable.
I had to turn off bluetooth on my phone/turn it on again/then go through the voice options on the car to get to select device and then it paired up.
This is quite a hassle to have to do while driving. It should connect automatically.

 

My 2012 Ltd has been flaky like that at times, you will lose the audio or hands free telephone setup. Clear out the pairing and do the phone setup again and all is well (until it randomly messes up again).

 

The head unit used and system is quite archaic and challenging to setup. Adding contacts from the phone is very hard and only one at a time. It's a area where Toyota is very far behind in that generation.

 

Seems as though it's a safety hazard to me. Toyota should have put a firmware update to fix this ages ago.

 

not sure how it's a safety hazard as the annoying thing is that you must be totally stopped to go thru the lengthy phone setup process. Many a times I tried to re-pair my phone while at a stop light only to have the light turn green and needed to move before completing the whole thing Head unit voice taunts you with "this feature is not available while vehicle is in motion"

 

I enquired with a dealer after getting mine which I bought used from a dealer. Never any firmware update to it. At least not the standard one, ones with NAV usually have updates as the maps need to be uploaded. Firmware accompanies them at the same time if a change is made.

I used SAT a lot, SiriusXM here.

 

My main issue with the stock head unit was the poor bluetooth sound quality for both music and phone calls. I fixed it by putting in a Sony head unit.

 

Seriously have never once had an issue with our phones or the stock head unit. But, then I've only used it with Samsung phones. Yeah it's clunky but IDC. It can answer a call when I want, "Hey Google" can respond, my GPS in the phone sounds through fine as does Pandora. Does all I need to do

 

I'm on a pixel 5a. It seems to work correctly with other BT devices. It works great with my Highlander as well but only when the Highlander properly pairs with the phone.