What Language?

In real life during the war in what language would the two nationalities' have been communicating with each other? Would the Italians' have been speaking Greek,the Greeks' speaking Italian or would they have been talking a form of simplified English as was portrayed in the film?
For example in the scene where Captain Corelli is complimented upon his mandolin playing he says the beautiful ballad is one he has written & is called "Pelagia's Song" whereupon Mandras' mother Drosoula (the always excellent Irene Papas) looks alarmed & turns away.
Her son Mandras had admitted in a previous scene how he could not read nor write (which presumably applies also to his mother) & so with hindsight it is unlikely that either of them would be able to speak a foreign language either. Is it possible therefore that such a scene would have been spoken in Greek then at the time?
I know it is an unusual question but I am just curious thats all. :o)