In this article, we introduce a reference model for interaction semantics among communicating discrete systems to guide the discourse on interoperability. The necessary set of unifying concepts is small and comprises essentially the notion of discrete systems interacting by exchanging information. It is based on a simple, but nevertheless complete classification of system interactions with respect to information transport and processing. Information transport can only be uni- or bidirectional and information processing is subclassified along the binary dimensions of state, determinism and synchronicity. For interactions with bidirectional information flow we are able to define a criterion for a layered structure of systems: we name a bidirectional interaction "horizontal" if all interacting systems behave the same with respect to state, determinism and synchronicity and we name it "vertical" --- providing a semantic direction --- if there is a behavioral asymmetry between the interacting systems with respect to these properties. It is shown that horizontal interactions are essentially stateful, asynchronous and nondeterministic and are described by protocols. Vertical interactions are essentially top-down-usage, described by object models or operations, and bottom-up-observation, described by anonymous events. The reference model thereby helps us to understand the significant relationships that are created between interacting discrete systems by their interactions and guides us on how to talk about discrete system interoperability. To show its conceptual power, we apply the reference model to assess several other architectural models, communication technologies and so called software design or architectural styles like SOA and REST.