<p>AI-enabled tools increasingly influence clinical decisions, patient journeys, and digital health services, yet many deployments struggle with opaque decision-making, fragmented governance, and limited engagement with clinicians and patients. This article presents a structured narrative review and conceptual capability-centric framework for responsible healthcare AI that treats AI not as a monolithic system, but as a set of modular capabilities to be understood, integrated, and governed within human-centred care pathways. The framework organises design and governance work into three phases: understanding AI capabilities in clinical and organisational context, harvesting capabilities into transparent and controllable service touchpoints, and improving systems through ongoing monitoring, feedback, and governance routines. Drawing on research in human-centred AI, explainable AI, health AI ethics, and human-AI interaction, we show how this approach supports participatory design with clinicians and patients, aligns AI behaviour with institutional responsibilities, and helps teams manage risks related to trust, bias, and digital wellbeing. We illustrate the framework with healthcare-oriented scenarios and discuss how it can complement technical advances in explainability and validation by providing a practical structure for multi-stakeholder collaboration, accountable deployment, and continuous improvement of AI-driven healthcare services.</p>