The Internet of Medical Things (IoMT) workflow applications have been rapidly growing in practice. These internet-based applications can run on the distributed healthcare sensing system, which combines mobile computing, edge computing and cloud computing. Offloading and scheduling are the required methods in the distributed network. However, a security issue exists and it is hard to run different types of tasks (e.g., security, delay-sensitive, and delay-tolerant tasks) of IoMT applications on heterogeneous computing nodes. This work proposes a new healthcare architecture for workflow applications based on heterogeneous computing nodes layers: an application layer, management layer, and resource layer. The goal is to minimize the makespan of all applications. Based on these layers, the work proposes a secure offloading-efficient task scheduling (SEOS) algorithm framework, which includes the deadline division method, task sequencing rules, homomorphic security scheme, initial scheduling, and the variable neighbourhood searching method. The performance evaluation results show that the proposed plans outperform all existing baseline approaches for healthcare applications in terms of makespan.