Disclaimer, I have not watched all of these!
The ones I know of are:
Haru ga Kita - tells the story of a japanese retail worker that falls for a korean photographer (Kai from EXO)
Massan - based on the real life story of a japanese man and his scottish wife who opened up a distillery in Hokkaido and became the first japanese producers of whiskey
I know of one other series that might interest you; it doesn't show the interracial relationship in the show but focuses a lot on the cultural differences: My Brother's Husband, which is about the canadian widower of a japanese man going to live with his husband's twin brother to find out about his husband's past. It explores the differences between Japanese and Western views on homosexuality.
Edit:
Looking into the foreign actors' profiles I also found this:
Our House - Japanese man remarries a american woman. Drama centers around the daughter's trying to kick her stepmother out and her relationship with her new stepmother