IT support for distributed and collaborative workflows as well as related interactions between business partners are becoming increasingly important. For modeling such partner interactions as flow of message exchanges, different top-down approaches, covered under the term interaction modeling, are provided. Like for workflow models, correctness constitutes a fundamental challenge for interaction models; e.g., to ensure the boundedness and absence of deadlocks and lifelocks. Due to their distributed execution, in addition, interaction models should be message-deterministic and realizable, i.e., the same conversation (i.e. sequence of messages) should always lead to the same result, and it should be ensured that partners always have enough information about the messages they must or may send in a given context. So far, most existing approaches have addressed correctness of interaction models without explicitly considering the data exchanged through messages and used for routing decisions. However, data support is crucial for collaborative workflows and interaction models respectively. This paper enriches interaction models with the data perspective. In particular, it defines the behavior of data-aware interaction models based on Data-Aware Interaction Nets, which use elements of both Interaction Petri Nets and Workflow Nets with Data. Finally, formal correctness criteria for Data-Aware Interaction Nets are derived, guaranteeing the boundedness and absence of deadlocks and lifelocks, and ensuring message-determinism as well as realizability.