PC is correct. You can't do it. The headset has its own "sound card" built in to convert digital signals from the PC into analog to drive the headphones, and convert the mic signal from analog to digital. The signals at the cable are digital. The 3.5 mm ports are analog. They are not compatible, period.
It is possible to get an ACTIVE converter to convert the digital signals to analog to put them into your sound card, but that would be silly. The PC would generate a digital signal, the sound card would convert it to analog, the active box would convert it back to digital with a loss of quality, and then your headphones would convert it back to analog.
I strongly recommend that you either plug your USB headphones into a USB slot, or that you get analog headphones to plug into the analog input and output of your sound card. While what you are describing is possible, it is simply inelegant and inefficient, and will also reduce your sound quality.