In (Rouached, Godart and al. 2006; Rouached, Godart 2007), we have described the semantics of WSBPEL by way of mapping each of the WSBPEL (Arkin, Askary and al. 2004) constructs to the EC algebra and building a model of the process behaviour. With these mapping rules, we have described a modelling approach of a process defined for a single Web service composition. However, this modelling is limited to a local view and can only be used to model the behaviour of a single process. A series of compositions in Web service choreography need specific modelling activities that are not explicitly derived from an implementation. An elaboration of modelling is then required to represent the behaviour of interacting compositions across partnered processes. This elaboration provides a representation that enables us to perform analysis of service interaction for behaviour properties. The ability to perform verification and validation between execution and design, and within the process compositions themselves, is a key requirement of the Web services architecture specification. In this paper, we further the semantic mapping to include Web service composition interactions through modelling Web service conversations and their choreography. We describe this elaboration of models to support a view of interacting Web service compositions extending the mapping from WSBPEL to EC, and including Web service interfaces (WSDL) for use in modelling between services. The verification and validation techniques are also exposed. An automated induction-based theorem prover is used as verification back-end.