There actually is no such thing as a "transparent" background in video. Instead what you have is either 3 channel video (red, green and blue value for each pixel) or 4 channel (red, green, blue and alpha values for each pixel).
The Alpha channel provides details about how opaque each pixel should be, however unless the video player playing the video file supports reading this extra channel of data, it won't actually do anything special.
Generally, unless the background image will actually be different for different users, your best bet may be to actually import the portion of the graphic that will be behind the video and actually record the video with the background behind it. Then, when you position things together correctly, it will appear relatively seamless (though you have to be careful about the color encoding to make sure colors match.) There is also some possibility that people's players will apply a color profile anyway and thus make the video frame have a slight color alteration from the normal background.
Otherwise, the jquery-seeThru project that Professor Sparkle mentioned is probably the best bet.