Building a display system with depth - HUD (Iron-Man)
All you need for a 3D effect is different screens for each eye. You need a stereoscopic display, like an Oculus Rift. 

From your question it looks like you think a Rift wouldn't work because you're trying to get a HUD that looks like the one in your video. But you need to imagine that HUD from the point of view of Tony Stark, not from the view given in the video. To him, it looks like things floating out in front of him in 3D.

I'm one of those guys that bought the Rift on Kickstarter. Let me tell you, it is amazing. The resolution for first developer kit is crap, like playing a PlayStation One game. But the 3D effect and head tracking is incredible. If you were to modify a Rift type device to re-display video from stereo cameras mounted the the front of the device, and overlay your HUD on top of that, you'd be in business.

You can't use a transparent screen and display a HUD onto it without some very fancy optics in front of the display, because you can't focus that closely. The easiest solution is to watch a stereo video and add the HUD to it.