I have Focusrite Scarlett 2i2 and selected that option in Logitech 920c drop-down menu. When I record video, audio doesn't record.
 
I've recorded plenty through Cakewalk Sonar with DAW and mic without a problem.
I've recorded video with 920c's internal mic without a problem.
 
I've followed some suggestions I found online, like disabling the webcam's mic in Windows 10 Program & Features, unchecking RightSound in Webcam Controls, checked/unchecked sound options in Windows 10,...
 
When I speak into mic when recording video I can see green equalizer bars in Windows 10 Program and Features lighting up, but when playing back there's nothing, not even green bars in Windows 10 Playback under Program & Features.
 
If I open Cakewalk Sonar and try recording audio through that, FPS on video recording drops to 27.70, and I need it at it's full capacity.
 
Any ideas? Did you go through this before getting it to work?

I'm glad you resurrected this thread because I forgot to report back on it. I used the C920 on my new laptop and it worked perfectly indicating that it wasn't the camera.
 
I finally figured out what happened only in the last day or so. The C920 didn't have a very long cord on it so I plugged it into my usb hub. I knew it was a big no no when I did it but I assumed that since the video worked ok it couldn't be the issue. The usb hub was in fact the problem and it may also be the issue with your situation. If you aren't plugged into a hub then try different usb outlets on your computer. The other things to check are the recording resolutions and type of drivers it's using. I also have Focusrite interface and it seems to like ASIO drivers the best.
 
As for a one program solution I have been using Vegas Movie maker 15 pro by Magix. It has a capture feature that allows a nice recording of both audio and video. I was able to make it work with my Presonus interface and the C920. There seem to be a few bugs in Movie Maker 15 though when using the capture feature. In a few instances I had to unplug.re plug the usb camera for the software to see it. When it works though it's the bomb. No more using two apps and aligning audio. The really nice thing about Vags is it sees all my vst plugins too so I can sculpt the audio right in that program. Hope this helps.

I'm not sure if this will be helpful to anyone (might be outdated because maybe Win10 has better audio driver/routing options) and you'll have to listen to my droning voice and somewhat scattered speaking style but solved this issue a few years back with Voicemeeeter and made a loooong ass video describing how I did it.
 
Seriously it's like five hours long BUT there are timestamped links in the video description so you can navigate the "chapters". The Intro and Program Overview chapters could likely be skipped for most who already know a bit about said programs but all the stuff about routing Voicemeeter betwixt various programs and external hardware is cromulent.
 
https://www.youtube.com/watch?v=SXEtm5_M9HI
 
I do ramble and drone in that though. However if you can stay awake there's a lot to be gleaned about forcing said issues.
 
Cheers.

Try Open Broadcast Studio. It's free and has a number of options for the type of thing I think you're trying to achieve. I use it in conjunction with my Intel Realsense 3d scanning web cam for chroma keying.