This article addresses the adaptive bipartite event-triggered output consensus issue for heterogeneous linear multiagent systems. We consider both cooperative interaction and antagonistic interaction between neighbor agents in both fixed and switching topologies. An adaptive bipartite compensator consisting of time-varying coupling weights and dynamic event-triggered mechanism is first proposed to estimate the leader's state in a fully distributed manner. Different from the existing methods, the proposed compensator has three advantages: 1) it does not depend on any global information of the network graph; 2) it avoids the continuous communication between neighbor agents; and 3) it is applicable for the signed communication topology. Assume that the system states are unmeasurable, and we thus design the state observer. Based on the devised compensator and observer, the distributed control law is developed such that the bipartite event-triggered output consensus problem can be achieved. Moreover, we extend the results in fixed topology to switching topology, which is more challenging in that state estimation is updated in two cases: 1) the interaction graph is switched or 2) the event-triggered mechanism is satisfied. It is proven that no agent exhibits Zeno behavior in both fixed and switching interaction topologies. Finally, two examples are provided to illustrate the feasibility of the theoretical results.