Integrated electrical and heating systems (IEHSs) are promising for increasing the flexibility of power systems by exploiting the heat energy storage of pipelines. With the recent development of advanced communication technology, distributed optimization is employed in the coordination of IEHSs to meet the practical requirement of information privacy between different system operators. Existing studies on distributed optimization algorithms for IEHSs have seldom addressed packet loss during the process of information exchange. In this paper, a distributed paradigm is proposed for coordinating the operation of an IEHS considering communication packet loss. The relaxed alternating direction method of multipliers (R-ADMM) is derived by applying Peaceman-Rachford splitting to the Lagrangian dual of the primal problem. The proposed method is tested using several test systems in a lossy communication and transmission environment. Simulation results indicate the effectiveness and robustness of the proposed R-ADMM algorithm.