Actually i's quite easy with a mixer:
1 Connect audio out from pc to mixer CH 3/4
2 Connect mic to CH 1
3 Connect USB mixer to USB pc
4 Use a third party encoder and you're set to go.
I'm using radiocaster because it does support VST plugins. That way the microphone will also make use of the VST settings

. Also the mic button in radioboss does not work with this setup. You can for example set any input with nothing connected to it as mic in radioboss so you can use the microphone button to control the music loudness when you speak but it won't do anything else.
There should be another method also but i didn't tried it yet. I am able to send my microphone and music to skype using the FX send on the mixer and line in on pc without issues and let listeners hear what the person on skype is saying with a usb soundcard (also audio out) to CH 5/6.
It should be possible (didn't tried this) to connect the FX send to the line in on the pc, turn all the FX knobs on the mixer to 0 (because you will send all that audio to the line in) except the one with the mic on it. In radioboss at the input settings you will be able to choose that line in and your mic should be working in RadioBoss when you press the mic button... but i'm affraid the mic wil work all the time unless you have a mute button for the microphone channel or put the volume on the mixer to 0 when you're done talking.