I was watching a documentary about a Lufthansa A380, and they said that the pilot and co-pilot are required to eat different meals; why is that?
Is it a country-specific requirement, or airline-specific?
It is a company specific rule found in the Flight Operations Manual so is airline specific. There is usually a statement that goes along with it which also says to avoid foods with a higher than typical rate of food poisoning, such as raw fish before and during the Flight. In the US, the FOM is submitted to, and accepted by the FAA so the procedures become required.
Although I have no reliable sources to this, I believe that pilots have to eat different meals to avoid food poisoning and therefore becoming sick mid-flight.
As for drinks, it should not matter as long as they drink from separate bottle / can.
EDIT: According to this article, it is not in FAA's policy for the pilots to eat different meals. However the airlines can still choose to make some kind of rule.