an interface between A and B must belong to either A or B or both, while a layer between A and B must be a third thing that is neither part of A or of B?
I wouldn't say that an interface must belong to either A or B, but a layer between A and B is definitely a third thing apart from either A or B. "Interface" is kind of an abstract concept; it is a set of rules governing the communication between objects A and B and thus isn't an object itself (although those rules are generally codified by one of the two objects.) A layer however is itself a distinct object or collection of objects related in purpose.
Thing is, the term "interface" depends on more context than just "in computer science". For example, computer scientists often speak of the interface between classes/code modules, but they may also speak of the human-computer interface between the user and the program. The definition of "interface" in each case is slightly different: the former is talking about the public methods or other messaging systems used by the code modules, while the latter is talking about the actual software and hardware widgets that the user is interacting with.