This paper presents a methodology for interoperability testing based on contextual signatures and passive testing with invariants. The concept of contextual signature offers a framework to add information on the states, the values of parameters, as well as logical connectors that increases the expressive power of invariants. This allows expressing horizontal and vertical interoperability properties, i.e., between layers of a protocol stack or end-to-end communication between distant entities. In order to test interoperability, we have defined a correlation algorithm between the events collected from different network views (client or network side). Once the correlation has been performed, we apply the contextual signatures that characterize interoperability properties to check their validity. To illustrate the application of the proposed approach, a real case study is proposed: the Wireless Application (WAP) protocol. The results of the experimentation performed on this protocol are also presented