Enterprise Information Systems (EIS) supporting Business Processes (BPs), particularly Sensitive Business Processes (SBPs), should be characterized by integrity, flexibility, and interoperability. However, the urbanization approach, which we rely on to implement these systems, must address the “three fit” problems that hinder the realization of these desired features at both the business and technical infrastructures: “vertical fit” problems – concerning the business infrastructure; “horizontal fit” problems and “transversal fit” problems – concerning the technical infrastructure. We argue that for overcoming those problems, it is necessary to define an explicit framework for specifying BPs/SBPs. We present in this paper our conceptual specification for the BPs/SBPs modeling domain in the form of a core domain ontology, in order to overcome “horizontal fit” and “transversal fit” problems. Specifically, we introduce (i) our reference ontological framework and (ii) provide an overview of the Core Ontology of Sensitive Business Processes (COSBP). Our focus lies in the representation of SBPs in order to overcome “vertical fit” problems.