I know this is an old thread, but I just went through trying to figure this out myself with Audacity. I found that in my audio devices, the "Stereo Mix" was hidden as a disabled device, so wasn't selectable by Audacity, but when enabled will give you the ability capture the enhanced audio.
To be specific, to enable the stereo mix, right click on the speaker icon from the taskbar and choose Recording devices.(There's multiple ways to get here, but this is quickest). You should see the Line 1 breakaway device. If the Stereo Mix isn't show, right click and check the "Show disabled devices" and see if stereo mix shows up. If it does, right click it, and enable it.
Now in Audacity, I have to choose the "MME" Audio Host and now can record the enhanced audio. Previously, only the Windows WASAPI was functioning, and simply recording the input audio, not the breakaway enhanced audio.
Good Luck!