Try choosing a specific device in Settings, Audio, Desktop Audio Device and see if that helps. I have a capture card and this works for me without any complex config. I set my Desktop Audio Device to My Speakers on my streaming PC. On my capture card I set Audio Output to Capture Only - capture card audio only goes to my Steam/Recording. Change Audio Output to WaveOut, I can hear my audio on my streaming PC and can hear the audio in my Stream/Recording. One note you have to have your Desktop Audio enabled in your Stream/Recording, if you have it muted you won't hear the capture card audio. This is just the way it works currently.
If you are seeing something different then let us know and provide a log of your streaming session.