"Parmi" literally translates to among, while "entre" means between. E.g.: When three people are sitting on a bench only the person in the middle would be considered as being in between, or "entre". When the same three people are sitting on the same bench in the same order, any one among ("parmi") them can be French. Or something. Basically, "entre" implies certain positioning and order, while "parmi" does not.
Good explanation. Being the French language, it follows that there is an exception.
Being present in a uniform, defined group can take entre even though no position or order is involved. The man was among/entre the troops, the women etc. Being in the defined group constitutes being between. (in French)