Embedded systems are a key enabling technology for the recent vast increase in functionality of a huge list of critical infrastructures. Hybrid automata can be used to model system-level behaviors for the large category of systems that exhibit strong couplings between discrete and continuous dynamics. Many software tools have been developed for hybrid automata to enable model-based design of embedded systems and these software tools are constructed by using their own modeling languages. Model-based design frameworks, such as Model-Integrated Computing (MIC), Model Driven Architecture (MDA), and Model Driven Design (MDD), have been advocated to raise the level of abstraction in software tool design by placing stronger emphasis on the use of software models in the software tool design process. In particular, MIC places strong emphasis on the use of Domain Specific Modeling Languages (DSMLs) and model transformations in design flows. Practical and effective development of formal specifications for DSML semantics within model-based tools can be challenging, but could positively impact adoption and reuse of these tools. The semantic anchoring methodology was developed to address this challenge by formally tying DSMLs to a ?semantic unit?, which is a formal specification that captures the operational semantics of a specific model of computation. Leveraging our prior work with semantic units, we develop a semantic unit for hybrid automata. In this paper, we explicitly specify the operational semantics of hybrid automata, and develop the corresponding semantic unit and model transformation rules. We demonstrate the effectiveness of the infrastructure in a practical case study involving the hybrid automata DSMLs, HyVisual and ReachLab.