The problem isn't EMI, I can tell you that now. I used to get exactly the same problems - my current fix is not perfect, but it will do.
I assume you are using your case's front panel audio jacks for your headset/microphone+headphones. The problem is that some, if not most cases (Antec is particularly notorious) bridge the ground connectors of the audio, USB and eSATA ports (along with any others that may be there). You obviously didn't notice the problem with motherboard audio - USB, eSATA and everything else comes from there, so the ground was shared anyway. Using a separate soundcard with a different supply of power means that there is current flowing through those connected ground rails. This creates your noise, in both microphone and headphone ports.
My case is an Antec 1200. My (hopefully temporary) solution was to disconnect the USB and eSATA headers from the motherboard, as well as disconnect the connector to the case. The noise issue stopped. I tried only connecting back the USB, or just the eSATA, but I got noise in every case. Although it is a shame to loose two front USB ports I have a card reader with a USB port, so it does the trick for now.
A more permanent solution would be to take out the whole front panel assembly, open it up then cut the connecting ground wires that join up the audio and USB/eSATA ports. Here
is a guy who did exactly this. I haven't quite got the nerve to attempt it yet...
Hope this helped