Dave, if you were to look at a picture of a half moon and a picture of a full moon, and compare the two, you would be able to see that the moon hasn't "disappeared" or that half the moon is missing, it's just partially in shadow...
According to this video the other side of the moon does not exist.
It would be impossible to see the sky where the other half should be if it did exist.
--Dave
Notice the circular Mare in the top right of each image. It's the same one in both. The one next to it to it's left is the same one in each image.
As for the reason why in the video it looks like part of the moon isn't there?
Well, like I said, that's because it's in shadow, not to mention that when you have a dimmer object in the background, but a brighter object in the foreground, it's almost always extremely difficult to see what's behind the brighter object. The brighter object in that video is the atmosphere, which is refracting blue light (just Google "why is the sky blue"). The amount of light being refracted is greater than any light being reflected on the dark side of the moon, but is not greater than the amount of light being refracted on the side of the moon facing the sun.