Different modeling formalisms for timed and hybrid systems exist, each of which addresses a specific set of problems, and has its own set of features. These formalisms and tools can be used in each stage of the embedded systems development, to verify and validate various requirements. The Compositional Interchange Format (CIF), is a formalism based on hybrid automata, which are composed using process algebraic operators. CIF aims to establish interoperability among a wide range of formalisms and tools by means of model transformations and co-simulation, which avoids the need for implementing many bilateral translators. This work presents the syntax and formal semantics of CIF. The semantics is shown to be compositional, and proven to preserve certain algebraic properties, which express our intuition about the behavior of the language operators. In addition we show how CIF operators can be combined to implement widely used constructs present in other timed and hybrid formalisms, and we illustrate the applicability of the formalism by developing several examples. Based on the formal specification of CIF, an Eclipse based simulation environment has been developed. We expect this work to serve as the basis for the formal definition of semantic preserving transformations between various languages for the specification of timed and hybrid systems.