...my husband started watching awhile back and wants to revisit, but can't remember the name of.

He's not sure if it originated in Japan or Korea, but he described it as follows:

"The lead female is the daughter of a Mafia boss, and she somehow gets in trouble with the mafia and is sent away. Either to Japan, if it was a K-drama or to Korea, if it was a J-drama. Once there, she meets a bumbling criminal guy. There's romance brewing between those two, also an interpreter chick, and there were a lot of fight scenes."

Omg, THANK YOU! He thinks that's it (naturally, he said TV show but it looks like maybe a movie). No wonder my GoogleFu failed me! Haha