Healthcare information exchange is an important research topic, which can benefit both healthcare providers and patients. In healthcare data sharing, many cloud-based solutions have been proposed, but the trustworthiness of a third-party cloud service is questionable. Recently, blockchain has been introduced in healthcare record sharing, which does not rely on trusting a third party. However, existing approaches only focus on the records collected from medical examination. They are not efficient in sharing data streams continuously generated from sensors and other monitoring devices. Today, IoT devices have been widely deployed and sensors and mobile applications can monitor patients' body conditions. The collected data are shared to laboratories and institutions for diagnosis and further study. Moreover, existing approaches are too rigid to efficiently support metadata change. In this paper, an efficient data-sharing scheme is proposed, called MedChain, which combines blockchain, digest chain, and structured P2P network techniques to overcome the above efficiency issues in the existing approaches for sharing both types of healthcare data. Based on MedChain, a session-based healthcare data-sharing scheme is devised, which brings flexibility in data sharing. The evaluation results show that MedChain can achieve higher efficiency and satisfy the security requirements in data sharing.