With the feature of convenience and low cost, remote healthcare monitoring (RHM) has been extensively used in modern disease management to improve the quality of life. Due to the privacy of health data, it is of great importance to implement RHM based on a secure and dependable network. However, the network connectivity of existing RHM systems is unreliable in disaster area because of the unforeseeable damage to the communication infrastructure. To design a secure RHM system in disaster area, this paper presents a Secure VANET-Assisted Remote Healthcare Monitoring System (SVC) by utilizing the unique “store-carry-forward” transmission mode of vehicular ad hoc network (VANET). To improve the network performance, the VANET in SVC is designed to be a two-level network consisting of two kinds of vehicles. Specially, an innovative two-level key management model by mixing certificate-based cryptography and ID-based cryptography is customized to manage the trust of vehicles. In addition, the strong privacy of the health information including context privacy is taken into account in our scheme by combining searchable public-key encryption and broadcast techniques. Finally, comprehensive security and performance analysis demonstrate the scheme is secure and efficient.