This article considers the bipartite time-varying output formation-containment tracking control issue for general linear heterogeneous multiagent systems with multiple nonautonomous leaders, where the full states of agents are not available. Both cooperative interaction and antagonistic interaction between neighboring agents are taken into account. First, an observer is constructed using the output information to observe the state information. Then, based on the information between neighboring agents, an independent asynchronous fully distributed event-triggered bipartite compensator is put forward to estimate the convex hull spanned by the states of multiple leaders. Note that the compensator does not require to use of any global information. Subsequently, a formation-containment tracking control strategy based on the observer and compensator and an algorithm to determine its control parameters are given. The Zeno behavior is further proved to be excluded in any finite time. In addition, a novel self-triggered control strategy based only on the sampled information at triggering instants is also formulated, which avoids continuous communication among agents. Finally, a numerical example is given to validate the effectiveness and performance of the proposed control strategies.