Recent advancement in the Internet of Medical Things (IoMT) allows patients to set up smart sensors and medical devices to connect to remote healthcare setups. However, existing remote patient monitoring solutions predominantly rely on persistent connectivity and centralized cloud processing, resulting in high latency and energy consumption, particularly in environments with intermittent network availability. There is a need for real-time IoMT computing closer to the dew, with secured and privacy-enabled access to healthcare data. To address this, we propose the DeW-IoMT framework, which includes a dew layer in the roof-fog-cloud systems. Notably, our approach introduces a novel roof computing layer that acts as an intermediary gateway between the dew and fog layers, enhancing data security and reducing communication latency. The proposed architecture provides critical services during disconnected operations and minimizes computational requirements for the fog-cloud system. We measure heart rate using the pulse sensor, where the dew layer sets up conditions for remote patient monitoring with low overheads. We experimentally analyze the proposed scheme's response time, energy dissipation, and bandwidth and present a simulation analysis of the fog layer through the iFogSim software. Our results at dew demonstrate a reduction in response time by 74.61%, a decrease in energy consumption by 38.78%, and a 33.56% reduction in task data compared to traditional cloud-centric models. Our findings validate the framework viability in scalable IoMT setups.