Healthcare networking and computing infrastructure is rapidly changing from closed environments to open environments that incorporate ubiquitous medical devices and novel application scenarios. For example, home-based healthcare involves the collection and analysis of data from pervasive sensors (often in real time) to guide therapy or to perform medical interventions. In this article, we address the challenges of data interoperability and regulatory compliance when designing and deploying healthcare applications in a heterogeneous home-edge-cloud environment. We propose the ChainSDI framework that leverages the blockchain technique along with abundant edge computing resources to manage secure data sharing and computing on sensitive patient data. We implement programmable ChainSDI application programming interfaces to facilitate the specification of home-based healthcare services running on a software-defined infrastructure (SDI). This article is a collaboration between computer scientists, medical researchers, healthcare IT professionals as well as healthcare providers with the goal of increasing the availability of SDI infrastructures while meeting the performance and regulatory requirements of healthcare applications. Our prototype demonstrates the feasibility of the framework and serves as a testbed for novel experimental studies in the context of emerging healthcare applications.