Throughout the 14th episode of Firefly and the following movie there are many Chinese phrases strewn about.
What are all of the Chinese phrases in Firefly/Serenity?
Looks like someone else thought about this and created a website.
There should be a translation for all the phrases used in Firefly. You can search by title or by phrase.
Chinese translations with standard Hanyu Pinyin romanization and Chinese characters for Firefly the TV series and Serenity the movie and comic books