Keep in mind that this list will feature White and Asian couples. I don't know of any movies where it's other interracial couples.
1.) Neo and Trinity in the Matrix trilogy
Technically Keanu Reeve's character is suppose to be a Caucasian man named Thomas Anderson/Neo, however Keanu Reeves is actually Eurasian in real life. He is Chinese, native Hawaiian, English and Portugese. In the Matrix his character falls in love with a Caucasian woman named Trinity played by Carrie Anne Moss.
2.) The Crying Freeman and Emu O' Hara in the movie called "The Crying Freeman"
The protagonist, a Japanese man played by Mark Dacascos falls in love with a Caucasian woman Emu O'hara, played by Julie Condra. The interesting thing is that in real life Both Mark and Julie would fall in love and get married. They have 3 children together.
3.) Jack Mcgurn and Lily Kawamura in Come See the Paradise
In this movie a Caucasian-American man falls in love with a Japanese American woman, eventually Jack is drafted into the army and his wife is interned in a internment camp. I'm not going to spoil the movie.
4.) Lyle Nomura and Katie Burrell in American Pastime
In this movie a Japanese American man and a Caucasian American woman fall in love with each other during WWII. The movie focuses on the Japanese American internment during WWII and the romance but it also briefly mentions the 442nd RCT.
5.) Lee Takkam and Ellie Linton in Tomorrow When the War Began
In this movie Australia is invaded and occupied by a fictional foreign country that speaks a made up language and has soldiers that wear uniforms that can be described as "futuristic third reich uniforms". The female protagonist is Caucasian woman named Ellie Linton, she falls in love with a Asian man named Lee Takkam.
6.) James and Emily in My Wedding and Other Secrets
A Caucasian man and Asian woman fall in love with each other in New Zealand. The Asian woman knows that if her father finds out about her feelings, she will be disowned.
7.) James Bond and Kissy Suzuki in You Only Live Twice
In this movie James Bond who is a Englishman falls in love with a Japanese woman who is also a spy. In the novel, it's said that James Bond had a child with her.
8.) Abby and Toshi in The Ramen Girl
In this movie, A Caucasian American woman and a Japanese man fall in love with each other.
9.) Bruce and Linda in Dragon: The Bruce Lee Story
In this movie about Bruce Lee, Bruce(A Chinese man) and Linda(A Caucasian woman) fall in love. It's a movie based on Bruce Lee's life.
10.) Liam and Adelaide in Shanghai Kiss
In this movie a Asian-American man and a Caucasian woman fall in love wit each other. This movie is a romance film.
11.) Sam and Amanda in Shanghai Calling
A Asian-American male attorney and a Caucasian woman fall in love with each other in Shanghai.
12.) Honorable Mentions
A lot of Jet Li's and Jackie Chan's characters have romantic relationships with non Asian women. Such as the movie called "The One" and "The spy next door."