Well it's not a perfect solution by any means and does give the final output a certain somewhat cartoony look. Basically it is a massive cheat!
The parallax is more effective in the distance (... hmm so maybe rendering the original image with a long lens may help ...) and there are limitations regarding areas that are obscured by overhangs becoming revealed (so for example a tree that hides terrain behind it would not be able to reveal the terrain because the terrain behind never got rendered.)
I'm using the depth pass in the render layers although if that is not available you could set up a second render and use a distance from camera to achieve the same result. This is then taken into photoshop and a threshold adjustment is run on it to create a black and white image to use as a mask on the cards. Changing the threshold creates different black and white images that push further away from the camera.
Initially I placed the cards at equal distances from the camera (in the z axis), that did not work well, then I placed them at twice the previous cards distance (1, 2, 4, 8, 16 ...), this worked much better. Lastly I tried measuring the distance of the hills in Terragen and using that as the card measurement. One extra step, all the cards have to be individually scaled to fill the camera screen space so the cards that are furthest away are much larger than the cards in the foreground.
That's pretty much it apart from setting a frame range and moving the camera a very small amount.
I used Nuke Non Commercial for this but I was originally going to use Lightwave. The process should work in any 3D capable package.
Hope this helps