I am almost sure Guitar Rig doesn't take in the audio from your computer and send it out its own headphone jack. Not totally sure, but that might be a dead end.

The first thing I would check is can you get both audio sources to play on the laptop speakers at once? Remove the headphones from the scene for a moment and just concentrate on "can I get two audio sources at once?"

It could be that your sound card is not capable of playing both audio sources through the computer headphone jack. If you are on windows, the audio settings would be in the control panel. You could check there.