If you're using a unified 3.5 jack, that's essentially what's going wrong.
There are rings on a 3.5mm jack that essentially are what it's for. Usually 2 green rings signifying L and R signal input for the headphones, and another seperate 3.5mm jack with a single pink ring for the mic. Xbox headsets unify this so you have one cable being plugged in.
PC's don't do that, they have a seperate mic and headphone slot, not a unified one. You'll need to buy a splitter which can split the single unified cable into the two seperate mic and headphone jacks.
Or you could get a new headset, as the one you have is pretty trash.