I didn't think I would have to explain the configuration of the jack on the end of a headset...
Actually, you are right; there was some confusion; I just read back and see that you are in fact using a single cord, not two. honestly I think I was personally confused by CC's post that references multiple connectors, when yours only has one.
have you ever plugged a headset into a cell phone?
No. I've never used a cellphone actually. (Amazing huh?) Sounds like... actually, I just did a quick google-
The connector used by cellphones looks like a standard phono cord (and in fact it has the same form factor) but is in fact a "TRRS" (Tip,Ring,Ring,Sleeve) connector, which contains 4 separate conductors for transferring analog data; so you've got left channel and right-channel for the headphone portion, and left channel and right channel for the microphone (although I imagine most headsets just have a single microphone and stuff the same signal into left and right) . Now, the problem is, Almost PC sound circuitry isn't wired for TRRS, it's wired for your standard 2-channel audio, so, as you note, you need an adapter.
Thankfully armed with the proper name it's a matter of googling... and we discover that CC was in fact right on the money. you need a headset adapter; this separates the four signals into two sets of two signals (one for mic, one for output).
Now that it's connected to the laptop (Mic connected to the Mic port on the laptop, the other one connected to the "headphone" port or to the line out depending on what you're after.) the only question is how you are trying to output.
Tricky, no idea what you're planning here, but there are splitters available- what you need is probably a TRRS Female to two TRS female adapters. I would imagine some of the various "headset adapter" solutions would work.