You say, "the other headphones had a combined mic and output". You MAY have one headset with a different connection system.
Look closely at the plug on the end of the cables from each headset. The common kind used with nearly all PC's has three contacts: Tip, Ring, and Sleeve. BUT the other kind used with many Apple systems and some phones uses a single plug with FOUR contacts: Tip, Ring1, Ring2, and Sleeve. That kind cannot work with a typical PC output socket. You need a particular adapter to convert that type into two 3-contact male jacks.
So IF you have one of those 4-contact systems on the headset that does NOT work, post here and we can advise what you need.