Solved!
Hey everyone, I had the same issue. I had to figure out the solution on my own, and I want the Blizzard community to have some help on this issue!
Here it is for all of you:
Go into Settings >
Sound >
Output Device >
Select your headphones (NOT hands free)
Go to Voice Chat (even if it is disabled)
Enable Voice Chat (even if you won’t use it)
Output Device >
Select your device (again, NOT hands free)
Enable Talking (again, even if you won't be talking)
Input Device >
Select anything that is not your headphones (note: you cannot select hands free, or standard)
This is a weird work-around, but it does work. If you are worried about chatting by accident, make sure the device you select in talk is muted in your sound settings, and make sure push-to-talk is enabled. If you are actually trying to talk to people, this will still work if the selected input device works.
FYI, this same work around works for Overwatch, for those of you who have a similarly muted computer when you try to join chat.
I just want to listen to music while playing games. Hope this helps you guys out too.
-Enjoy