Manned-unmanned teaming (MUM-T) is an emerging network system which interconnects manned aerial vehicles (MAVs) with unmanned aerial vehicles (UAVs) to enhance mission effectiveness and reduce workloads. Like other wireless systems, MUM-T is prone to attacks from the open communication channel. Therefore, an authentication scheme is required to establish secure and trusted communication between the MAV and the UAV. However, existing schemes fail to provide adequate security features and necessary efficiency, mostly due to their incomprehensive threat modeling and improper use of authentication techniques. Moreover, traditional centralized architecture of the authentication server leads to the single point of failure (SPOF) problem, which jeopardizes the robustness and scalability of MUM-T. In this paper, we propose a fault-tolerant authentication scheme for MUM-T that will solve these problems. To enhance its security, we construct a new threat model consisting of adversary's capabilities, security features, and security challenges to ensure the security of a scheme under combination attacks. To preserve the highest possible efficiency, we propose the design principle of using lightweight primitives for authentication and applying public key operations in key establishment. To address the SPOF problem, we employ a distributed fault-tolerant mechanism to share registration information within authentication servers and defend against faulty nodes. As is demonstrated by the security proof and performance comparison, our scheme succeeds in improving security and reducing overall costs, which provides a better solution than existing schemes.