The reliability of a character is based upon a few different things when looking at a character or a narrator. The things to examine, when trying to decide if a character/narrator is reliable, are dialogue, indirect characterization, direct characterization, and the character's private thoughts. On top of that, one must realize that some will not agree with an individual's interpretation of character reliability. Character reliability is simply too subjective.
In regard to Hemingway's short story Hills Like White Elephants, one needs to take into consideration a few things. First, the entire story contains mostly dialogue. Therefore, given that dialogue does not provide any true insight into a character's mind, one can easily conclude that the characters are not reliable. This is based upon the fact that no private thoughts for either of the characters are provided. (Private thoughts provide what a character is actually thinking about a conversation, another character, or what is going on around them.)
Outside of that, readers, over the course of the story, are left confused about the decision the characters make regarding the abortion. Readers are simply left hanging at the end of the story without closure.
One last thing that readers need to consider is the fact that the characters remain unnamed. One can assume that Hemingway chose not to name the characters (although the American refers to the girl as Jig, readers know that this is a nickname) in order to keep them anonymous. This being said, the fact that readers cannot associate a true name for each of the characters provides another justification regarding the unreliability of the characters.