This is a HUGE pain. Currently windows doesn't have any support for this in settings.
Your sound card doesn't have any option for it natively either.
Some people get an additional audio card, they seem to have good luck with that. I don't know the details of how exactly they set it up, but adding a second device seems like the best solution.
Others are able to get software solutions to accomplish this. I tried this, and it worked alright enough i guess, but was very picky and burdensome, plus they want you to pay for their bulky software.
I ended up trashing the idea and setting up the fiance's PC to the TV as she never watches TV and uses the PC at the same time.