This paper proposes a novel edge-event-triggered sliding mode control strategy to achieve consensus of heterogeneous multi-agent systems (MASs) consisting of the first-order and second-order agents under the influence of unknown disturbances. The edge-event-triggered mechanism (EETM) is uniquely defined and differs from traditional node-based approaches by focusing on individual edges rather than nodes, resulting in more efficient communication. The edge-event-triggered mechanism utilizes the relative positions between an agent and its neighbors, independent of global coordinates. The designed controller has two components. First, the sliding mode control strategy enables heterogeneous MASs to reach and maintain their states on the sliding mode surface despite unknown disturbances. Subsequently, the equivalent control strategy, combined with the edge-event-triggered mechanism, guarantees the consensus of heterogeneous MASs while avoiding Zeno behavior. Triggering functions are developed for agents that form the same edge, allowing asynchronous mechanisms triggered by events of the edge. By employing the Lyapunov stability theory, sufficient conditions for the proposed control strategy are given. Simulation results demonstrate the effectiveness of the theoretical results, showing significant communication reduction compared to traditional event-triggered approaches.