When you plug-in a headphone or earphone into a PC, it takes over the playback sound and mutes the big speaker. That's because both audio pass through the same audio card. It's possible to have a separate audio output if you are using a USB headset (w/ mic) for making skype calls. USB headsets have a built-in soundcard and appears as a separate device in Control Panel>>> Sound>>> Playback tab. I just tested it again and it works the way you want it to work on your post above. So you might want to invest on a USB headset. Mine is a Logitech Clear Chat Pro.
Edited by badr0b0t, 06 June 2014 - 10:35 PM.