Coordinated multi-vehicle autonomous systems can provide incredible functionality, but off-nominal conditions and degraded system components can render this capability ineffective. This paper presents techniques to improve mission-level functional reliability through better system self-awareness and adaptive mission planning. In particular, we extend the traditional definition of health management, which has historically referred to the process of actively monitoring and managing vehicle sub-systems (e.g., avionics) in the event of component failures, to the context of multiple vehicle operations and autonomous multi-agent teams. In this case, health management information about each mission system component is used to improve the mission system's self-awareness and adapt vehicle, guidance, task and mission plans. This paper presents the theoretical foundations of our approach and recent experimental results on a new UAV testbed.