Recording the screen when it includes a video playback shouldn't be a problem. The frame rate may not keep up, but the image should be there if a bit choppy.
Perhaps you see a black box where the video from your webcam would appear? This is the same when you do a static print screen capture. If so, you need to change your display settings. Right click somewhere on the desktop and navigate to your display settings, look for the advanced tab, troubleshooting and then reduce the hardware acceleration until the directX drivers are disabled (about 50%).
Here's help from another source (http://www.snagitguide.com/67/snagit-black-screen). Hope it solves your problem.
