Virgin Snow - movie, she's Japanese and he's Korean
The Lover - drama, one of the four couples involves one Korean guy and one Japanese guy (both speak Korean + the Japanese guy speaks and teaches some Japanese)
Seducing Mr. Perfect - movie, the leads are both Korean, but the male lead, being an overseas korean, speaks English and the female lead speaks Korean
Tamra, the Island - historical drama, the female lead is Korean from Jeju island and she meets a shipwrecked British guy who speaks only English, at least at the beginning (he's the second male lead, not the first, but the linguistic and cultural exchange is quite interesting and funny :D)