The integrated electricity-heat-hydrogen system (IEHHS) facilitates the efficient utilization of multiple energy sources, while the operational flexibility of IEHHS is hindered by the high heat inertia of alkaline electrolyzers (AELs) and the variations of renewable energy. In this paper, we propose a robust scheduling of IEHHS considering the bidirectional heat exchange (BHE) between AELs and district heating networks (DHNs). First, we propose an IEHHS model to coordinate the operations of AELs, active distribution networks (ADNs), and DHNs. In particular, we propose a BHE that not only enables the waste heat recovery for district heating but also accelerates the thermal dynamics in AELs. Then, we formulate a two-stage robust optimization (RO) problem for the IEHHS operation to consider the variability of renewable energy in ADNs. We propose a new solution method, i.e., multi-affine decision rule (MADR), to solve the two-stage RO problem with less conservatism. The simulation results show that the operational flexibility of IEHHS with BHE is remarkably improved compared with that only with unidirectional heat exchange (UHE). Compared with the traditional affine decision rule (ADR), the MADR effectively reduces the IEHHS operating costs while guaranteeing the reliability of scheduling strategies.