A cloud-based Artificial Intelligence (AI) service has recently empowered the Internet of Medical Things (IoMT) in many applications on the remote Human Interaction Recognition of Pervasive Healthcare Monitoring (HIR-PHM). In this work, a framework of the skeleton-based HIR-PHM under secure Edge-Fog-Cloud computing (EFCC) was proposed to manage the computation and storage resources, latency, cyber-attack, and privacy-preserving simultaneously. At the Edge, IoMT with a camera, record the human interaction as videos and sends them to the Fog, which installed a human pose estimation model, PoseNet, to convert the videos into human skeleton data. At the Cloud, a skeleton-based Spatial-Temporal Graph Convolution Network with Pairwise Adjacency Matrix (STGCN-PAM) was employed to recognize the human interaction. A Hybrid of One Time Password (OTP), Hashed Messages Authentication Code (HMAC), and symmetric cipher were employed to secure the skeleton data. The UT-Interaction dataset was used to evaluate the proposed framework. Besides, the computation performance and latency under EFCC were compared with Edge-Fog and Edge-Cloud deployments. Experimental results confirmed two major contributions: 1) the proposed framework has promising performance compared with other methods on the dataset. 2) The skeleton-based HIR-PHM with secure EFCC shows the advantages of better computation performance in terms of frame per second.