Difference between 前面 and 面前
前面 means "in front of" or "at the front of". It can be used for anything that has a front, though in some cases just 前 may be better.  

面前 means "in front of the face". It can only be used in the context of things that (literally or metaphorically) have a face. In many cases it carries a sense of "in the face of" or "in the view of". For example:

法律面前没有特权
There are no privileges before the law.
如何在喜欢的人面前表现
How to present yourself before a person you like / are attracted to.


So your initial suspicion is right.

You can use 前面 for a person, but only if you're strictly referring to the position, and not to the sense of "looking at". For example, you could use 前面 when you want to say "there are many people in front of me in the line" but not when you say "The student is standing in front of the teacher", where 面前 would be more appropriate.