Use "between" to describe a relationship of two things or more than two things if those things are considered pairwise. Otherwise, use "among." You say
between a rock and a hard place
because there are only two alternatives -- rocky and difficult. But you'd also say
I've got lint between my toes
never "among my toes," even if you've got the full complement of ten toes. And
There is agreement between John, Joe, and me
is fine if the John and Joe agree to the same thing that John and I agree to, also being the same thing that Joe and I agree to.
In the OP's example, the USSR, the US, the UK (and actually, France) agreed between them to divide Berlin among them. Every one of the allies agreed with all the others about how to split the city, but zones were parceled out to the group.