This is only possible if you've got two different hardware for audio, like the built-in sound chip of your motherboard, and a dedicated sound card plugged into your motherboard. Once you have that, you'll then have to go to each app's settings and choose where you want to send its sound to.
For instance, you set iTunes to send its sound to your motherboard sound chip, since you'll most likely plug in your USB headphones into your motherboard's port. Then plug in your speakers to your dedicated sound card, and set the app to send its sound there.
I'm not really sure if you can get all your sound to broadcast through both the speakers and headphones at the same time though.