This paper presents an integrated approach for modelling enterprise architectures using UML. To satisfy a need for a wide range of modelling choices, we provide a rich set of process-based and role-based modelling concepts, together with a flexible way of associating business events with business processes and roles. Our approach enriches Unified Modelling Language (UML) to support the requirements of enterprise distributed object computing (EDOC) systems and is currently being considered by the Object Management Group (OMG) for standardisation.