The operational backbone of modern organizations is the target of business process management, where business process models are produced to describe how the organization should react to events and coordinate the execution of activities so as to satisfy its business goals. At the same time, operational decisions are made by considering internal and external contextual factors, according to decision models that are typically based on declarative, rule-based specifications that describe how input configurations correspond to output results. The increasing importance and maturity of these two intertwined dimensions, those of processes and decisions, have led to a wide range of data-aware models and associated methodologies, such as BPMN for processes and DMN for operational decisions. While it is important to analyze these two aspects independently, it has been pointed out by several authors that it is also crucial to analyze them in combination. In this paper, we provide a native, formal definition of DBPMN models, namely data-aware and decision-aware processes that build on BPMN and DMN S-FEEL, illustrating their use and giving their formal execution semantics via an encoding into Data Petri nets (DPNs). By exploiting this encoding, we then build on previous work in which we lifted the classical notion of soundness of processes to this richer, data-aware setting, and show how the abstraction and verification techniques that were devised for DPNs can be directly used for DBPMN models. This paves the way towards even richer forms of analysis, beyond that of assessing soundness, that are based on the same technique.