How do I get sound through the HDMI cable AND all my ext. sound jacks?

I just built a new budget gamer rig (first build ever) and everything is working fine on the video card (ATI Radeon 5670). I got sound coming across the HDMI cable just like it's supposed to be. Only problem is, when you fix it so sound comes through the video card and down the HDMI cable, you loose sound to ALL your external sound jacks. How you gonna use a head set and the HDMI cable at the same time? The video card does not have any type of audio connector that plugs into the Mobo, so the audio must be getting channeled through the PCIe slot I think? There's gotta be a way to get sound through the HDMI cable and to all the external audio jacks simultaneously. Would this be a driver issue? Or would I need to go the route of insalling a sound card? Would that even work? Or would I still have the same problem?

The thing seems like such a simple issue. It would be surprising to me if the companies who make these components didn't have this thing figured out yet.