"Chan is a diminutive suffix; it expresses that the speaker finds a person endearing. Thus, using chan with a superior's name would be condescending and rude. In general, chan is used for babies, young children, and teenage girls. It may also be used towards cute animals, lovers, and close friends. "
It's otaku humor.
In Japanese ... his wife is ethnically Chinese.
Doesn't matter in the context of the joke. Has nothing to do with his wife, only 'chan'.