The sentence "See you on the other side." is often used in movies and series, for example Lost, Jason Bourne movies and many others.
Is this a reference to an old movie? Or is it just a common phrase in English?
Most likely this reference started it's life out as a reference to the astronauts conversation during the Apollo 8 mission, as they passed behind the moon for the first time:
CapCom Gerry Carr spoke to the three astronauts more than 200,000 miles away, "Ten seconds to go. You are GO all the way." Lovell replied, "We'll see you on the other side", and Apollo 8 disappeared behind the Moon, the first time in history men had been occulted. For 34 minutes there would be no way of knowing what happened.
Obviously this line has been used a lot in various other places since (books, movies, TV shows, even music) and is usually said before people part ways to pass an otherwise difficult objective, whether that be said by Jason Bourne just before a mission or just before stepping through the Stargate for the first time.
"See you on the other side" is also a reference to the afterlife. It was possibly used in reference to the River Styx and the crossing of such river into the afterlife. This was the meaning Jim Morrison had when he wrote "Break On Through (To The Other Side)", which was released a year or so before the Apollo 8 mission.