At 0:52 of this video there is a scene where the vet and noob are in free fall due to a crashing airplane. Is there a level in this game where this takes place?
Yes, it is. It's in the fouth mission called "Turbulence" where you're playing a russian agent and have to protect the russian president and his daughter.
The weightlessness only lasts a few moments, but it's gameplay and not a video: you're able to fly around (limited), reload and shoot.