Cyberspace is becoming of increasing importance for providing healthcare services and this is leading to the special need for the protection and sustainability of e-health information infrastructure systems. The main goal of this paper is to develop a cybersecurity numerical assessment framework for e- health critical information infrastructure systems, as this leads to specifying the requirements for enhancing the cybersecurity protection of these systems. To- ward the achievement of this goal, the work involves the development of knowledge content specifically concerned with cybersecurity protection for e- health critical information infrastructure systems on the one hand; and with using this content to develop the targeted cybersecurity assessment framework for these systems on the other. The framework emphasizes providing metrics that deliver numerical measures for various cybersecurity protection issues involved. The work also considers illustrating the use of the framework for the assessment of the state of cybersecurity e-health critical information infrastructure case studies; in addition to highlighting how this assessment can help the improvement of this state. The developed and tested framework would contribute to cybersecurity as- sessment in general and would be specifically valuable to those concerned with cybersecurity for e- health critical information infrastructure systems.