MacBook Air and external monitor webcam

I use my MBA on a Dell external monitor in certain locations. Monitor works great via HDMI connector to Thunderbolt port (??). For the life of me, I could never understand why the external monitor webcam was not visible. I tried driver software and any idea I could research to solve. Then, I read a post that said HDMI is "one direction" and so it's video out. (This also explains why my native Mac monitor with webcam works...)

So, my question is this: Is there a solution that would allow the MBA to connect to the external monitor and recognize the built-in webcam? Or do I need to give up the ghost on this idea??

Thanks

John