In one of my previous posts, I referenced a film on the history of the White House called National Geographic: Inside the White House (click to watch for free online). This is not the film I had been thinking about, though it is an interesting view (watch out for a few bits of mature content). It's more technical and big-picture oriented than the one I had been thinking of.
The White House Revealed, from the Smithsonian Channel, seems to be the one I was remembering. You can also click this title to watch it for free online. This one is more personal - focusing on the stories of the White House as told by the White House staff. You might enjoy them both!