This paper studies a new type of fully distributed double event-triggered bipartite containment (DETBC) problem for linear multiagent systems (MASs). Meanwhile, multiple leaders with non-zero inputs and time-varying multiplicative and additive actuator faults (TMAAFs) are considered. First, in contrast to traditional event-triggered mechanisms (ETMs), the proposed novel double ETMs can guarantee that information transfer between agents and controller updates proceeds asynchronously. Some adaptive parameters are introduced in the trigger functions to enhance the dynamic adjustment ability of double ETMs. The trigger threshold depends on the relative state-dependent, which is independent of continuous information from neighbors. Then, a fault-tolerant DETBC protocol is designed to solve actuator fault problems. Moreover, compared with other relevant works, our control protocol is fully distributed, which avoids reliance on global information. Finally, a simulation experiment is conducted to validate the feasibility of the designed protocol.