An asynchronous heterogeneous decomposition (async-HGD) algorithm for integrated transmission and distribution networks coordinated optimisation considering communication conditions is proposed. Compared with traditional synchronous HGD (sync-HGD), a partial synchronisation mechanism is introduced instead of the full synchronisation to alleviate the influence of communication delays. Under this mechanism, the transmission system operator does not need to wait for the slowest distribution system operator to complete its subproblem and update boundary parameters before the next iteration can proceed. Also, a bounded delay is introduced under this mechanism to ensure sufficient freshness of all the updates. Further, the previous value strategy (PVS) and linear regression strategy (LVS) are applied to handle non-instantaneous interruptions in the communication networks as an improvement of the async-HGD. Numerical experiments show that considering communication delays in the actual operation; the async-HGD takes less time to converge compared with the sync-HGD under appropriate settings. In addition, PVS and LVS can both enhance the robustness of the overall algorithm by achieving approximate solutions, and the LVS can achieve more accurate results compared with the PVS.