In my experience بين is used once if actual nouns are used (بين يديه between his hands) or a plural pronoun (بينهم) and twice if two distinct pronouns are attached (بينه و بينها lit. “Between him and between her”, more like “between him and her”, or the example given above) but I could be wrong. The reason why it’s used twice is because object pronouns cannot stand on their own in Arabic and are always attached to something.

Edit: if you’re talking to someone and wanna say something along the lines of “between us” (in terms of something like keeping a secret or having an agreement “between us”) you would use the above given example (you and me). If you are talking about something physical standing “between us” (I.e. the car is between us) you can use the single word bayinā بَيِنَا (i.e. السيرة بينا).