The Smart and Connected Health (SCH) revolution is characterized by the convergence of technologies — from edge computing to cloud computing, Artificial Intelligence (AI), and Internet of Things (IoT) — blurring the lines between the physical and digital worlds. Although these are distinct technologies that evolved independently over time, they are becoming increasingly more intertwined in a way that the capabilities of the technologies are aligned in the best possible way. The public embracement of wearables and the integration of IoT provide greater availability, accessibility, personalization, precision, and lower-cost delivery of healthcare services. Bringing the power of AI offers the ability to wring insights from health data more quickly and accurately. Cloud-IoT has emerged to address some of the major challenges of IoT related to analytics, big data storage, scalability, management, reliability, and heterogeneity. Acting on real-time data compels a move towards edge/fog technology to meet the strict computing time requirement addressing the main drawbacks of Cloud-based IoT solutions. Although the convergence of the edge-fog-cloud in the age of IoT can potentially be a promising paradigm shift, its adoption is still in its infancy phase, suffering from various issues, such as lack of consensus towards any reference models or best practices. Thereby, this paper presents a holistic approach and reference architecture to address the interplay of edge-fog-cloud IoT for healthcare applications. Moreover, a Reinforcement Learning (RL) based offloading technique is presented to distribute the load across edge, fog, and cloud. Finally, a novel case study, ECG-based arrhythmia detection, is presented to better demonstrate and evaluate the efficiency of the proposed model.