Rising aggressive virus pandemics urge to conduct studies on dependability and security of modern computing systems to secure autonomous and continuous operations of healthcare systems. In that regard, we propose to quantify dependability and security measures of an Internet-of-Medical Things (IoMT) infrastructure relied on an integrated physical architecture of cloud/fog/edge (CFE) computing paradigms in this article. We propose a reliability/availability quantification methodology for the IoMT infrastructure using a hierarchical model of three levels: 1) fault tree (FT) of overall IoMT infrastructure consisting of CFE member systems; 2) FT of subsystems within CFE member systems; and 3) continuous-time Markov chain (CTMC) models of components/devices in the subsystems. We incorporate a number of failure modes for the underlying subsystems, including Mandel-bug related failures and non-Mandel bugs related failure, as well as failures due to cyber-security attacks on software subsystems. Five case-studies of configuration alternation and four operational scenarios of the IoMT infrastructure are considered to comprehend the dependability characteristics of the IoMT physical infrastructure. The metrics of interest include reliability over time, steady state availability (SSA), sensitivity of SSA wrt. selected mean time to failure—equivalent (MTTFeq) and mean time to recovery—equivalent (MTTReq), and sensitivity of SSA wrt. frequencies of cyber-security attacks on software subsystems. The analysis results help comprehend operational behaviors and properties of a typical IoMT infrastructure. The findings of this study can improve the design and implementation of real-world IoMT infrastructures consisting of cloud, fog, and edge computing paradigms.