How to remove any words containing two adjacent characters with different cases?

I have a list of permutations of ABCabc and I want to remove any permutations with two adjacent characters with different cases (uppercase and lowercase).

For example,

  • ABCcab is kept.
  • ABCacb must be removed because Ca contains two adjacent characters with different cases.
  • AbBcaC must be removed as well.

Attempt

Here is my attempt but without filtering.

Select[StringJoin /@ Permutations[Characters@"ABCabc"],....]