Is there a single word to describe a combination of a projected video and a live stage performance?

I would call such a performance multimedia.


What you describe sounds like an evolution of the sound and light show with the inclusion of live actors. (The term is a translation of the French son et lumière, because the concept of large-scale video projection accompanied by music was originally French -- for more, see http://en.wikipedia.org/wiki/Son_et_lumi%C3%A8re_(show) ).

'Multimedia' is not inaccurate, but it is a very general term that covers many other concepts.