The intelligent management of built cultural heritage, including heritage buildings, requires common semantics in the form of standardized ontologies to achieve semantic interoperability. Foundational ontologies should be reused when building new ontologies, as they provide high-level terms; however, candidate foundational ontologies should be evaluated for quality and pitfalls. Simple metrics (e.g., number of concepts) are easy to obtain with existing tools. Complex metrics such as quality of ontology structure, functional adequacy, transferability, reliability, compatibility, maintainability, and operability, are defined in recent ontology evaluation frameworks; however, these do not evaluate interoperability features. The paper proposes an improved framework for an automated ontology evaluation based on the OQuaRE framework. Our approach improved some of the metrics of the OQuaRE framework and introduced three metrics for assessing the interoperability of the ontology in question (Externes, Composability, and Aggregability). In the experimental section, the framework is validated in an evaluation of cultural heritage information ontology (CIDOC CRM—ISO 12217:2014) with the use of new software for ontology evaluation. The detailed results reveal that the ontology is minimally acceptable and that the improved evaluation framework efficiently integrated interoperability metrics. Recommendations for the improvement of the cultural heritage information ontology are described in the Discussion and Conclusions section.