Okay, getting the HP webcam running on Linux wasn't hard at all. Enable Video For Linux (CONFIG_VIDEO_DEV) which can be found in the Linux kernel configuration at Device Drivers, Multimedia Support. Then, select Video capture adapters and inside that menu, select V4L USB devices and then USB Video Class (UVC). Once installed, reboot (or load the kernel module) and ensure that your user is in the video group. You'll then be able to activate the webcam (for instance, using mplayer tv:// or using skype).

The integrated microphone is also no problem. It is by default muted, so using alsamixer, press F4 (to get to the capture menu) and unmute the channels + enable capturing (press spacebar).