"I will have an interview tomorrow" should be accepted!
In context, yes it should be understandable, but in a strict translation sense, I believe the correct way to express "I will have an interview tomorrow" is 我明天會有一个面试
面试; "noodle test"! Yeah, that's a pretty good description of "interview".
This is an example of a distinction that is lost due to the use of simplified characters. The traditional character for noodles is 麵, with the radical 麥 (mai-4th tone), meaning "barley/oats" (i.e. grain), and with 面 as the phonetic component.
In this case, 面 means face. An interview is a face-to-face, or in person, "test."
Shouldn't it be "I have a interview tomorrow
"An" is used before words that start with a vowel sound, and "a" is used before words that start with consonent sound.