The current information systems for the registration and control of electronic medical records (EMR) present a series of problems in terms of the fragmentation, security, and privacy of medical information, since each health institution, laboratory, doctor, etc. has its own database and manages its own information, without the intervention of patients. This situation does not favor effective treatment and prevention of diseases for the population, due to potential information loss, misinformation, or data leaks related to a patient, which in turn may imply a direct risk for the individual and high public health costs for governments. One of the proposed solutions to this problem has been the creation of electronic medical record (EMR) systems using blockchain networks; however, most of them do not take into account the occurrence of connectivity failures, such as those found in various developing countries, which can lead to failures in the integrity of the system data. To address these problems, HealthyBlock is presented in this paper as an architecture based on blockchain networks, which proposes a unified electronic medical record system that considers different clinical providers, with resilience in data integrity during connectivity failure and with usability, security, and privacy characteristics. On the basis of the HealthyBlock architecture, a prototype was implemented for the care of patients in a network of hospitals. The results of the evaluation showed high efficiency in keeping the EMRs of patients unified, updated, and secure, regardless of the network clinical provider they consult.