Effective healthcare delivery and research increasingly depend on the ability to share clinical data across organizational boundaries. However, fragmented systems, escalating cyber threats, and stringent regulatory requirements continue to limit secure and trustworthy health information exchange. Traditional perimeter-based security models, which assume implicit trust within institutional networks, are no longer adequate in modern, highly distributed healthcare environments. This paper presents a comprehensive framework for secure health data sharing grounded in continuous verification principles, layered encryption, and coordinated governance across participating institutions. The proposed architecture enforces verification of every access request regardless of user location, encrypts data throughout its lifecycle, and maintains detailed audit trails to ensure accountability and regulatory compliance. In addition, the framework supports privacy-preserving collaborative research through federated and distributed analysis models that allow institutions to generate shared insights without exposing individual patient records. Practical implementation strategies, governance structures, and phased deployment pathways are outlined to enable incremental adoption without disrupting clinical workflows. By integrating technical safeguards with organizational coordination, this framework demonstrates how healthcare organizations can balance data accessibility, patient privacy, and system security. The approach offers a scalable and practical foundation for advancing interoperable care, collaborative clinical intelligence, and public trust in health data exchange.