EDIT: it appears that the next version of three.js (R71) will have a simpler way to do this, so if you can use the dev branch (or just wait), you can do this much more easily. See this post: three.js transparent object occlusion
MY ORIGINAL ANSWER (without using the new features in R71):
I think the best way to do this is (to avoid extra work by creating new rendering passes for example) to modify the WebGL renderer (src/renderers/WebGLRenderer.js) and add support for a new kind of object, perhaps call them “occlusionObjects”.
If you look in the renderer, you will see two current object lists, opaqueObjects and transparentObjects. The renderer sorts the renderable objects into these two lists, so that it can render the opaque objects first, and then the transparent objects after them. What you need to do is store all of your new objects into the occlusionObjects list rather than those two. You will see that the opaque and transparent objects are sorted based on their material properties. I think here, you may want to add a property to an object you want to be an occluder (“myObject.occluder = true”, perhaps), and just pull those objects out.
Once you have the three lists, look what the render() function does with these object lists. You’ll see a couple of places with rendering calls like this:
renderObjects( opaqueObjects, camera, lights, fog, true, material );
Add something like this before that line, to turn off writing into the color buffers, render the occlusion objects into the depth buffer only, and then turn color buffer writes back on before you render the remaining objects.
context.colorMask( false, false, false, false);
renderObjects( occluderObjects, camera, lights, fog, true, material );
context.colorMask(true, true, true, true);
You’ll need to do this in a couple of places, but it should work.
Now you can just mark any objects in your scene as “occluder = true” and they will only render into the depth buffer, allowing the video to show through and occluding any opaque or transparent objects rendered behind them.