i am having the same issue and what i tried was get a cable from the local 99 cent store that has a headphone jack on one end and a yellow , red , white connectors on the other end. i plugged that in ( front mic ) and i got loud distorted sound i could hear while live streaming. it did effect the audio that was heard on the viewers end also. so it 50/50 if you want to tinker with that. but i agree we need a solution for this i jus searched back to the beginning of time and theres no fix or work around.
but in theory i think that program virtual audio cable will allow you to play on input audio to 2 seperate audio outputs. i dont know how to use virtual audio caable that well but heres the link to it if you want to give it a shot.
LINK REMOVED SO I DONT !@#% UP