We filmed a spokesperson on a green screen and have the video files ready in multiple formats.
With Flash we could use the wmode transparent within the param and em
Update: Webm with an alpha channel is now supported in Chrome and Firefox.
For other browers, there are workarounds, but they involve re-rendering the video using Canvas and it is kind of a hack. seeThru is one example. It works pretty well on HTML5 desktop browsers (even IE9) but it doesn't seem to work very well on mobile. I couldn't get it to work at all on Chrome for Android. It did work on Firefox for Android but with a pretty lousy framerate. I think you might be out of luck for mobile, although I'd love to be proven wrong.