Electric-heating integrated energy system (EH-IES) is pivotal for advancing energy structure reforms, and proper planning of EH-IES components can markedly enhance the operation economy, environmental sustainability, and system stability. Nonetheless, the inherent randomness and intermittency of renewable energy sources, along with the peak and valley characteristics of the load, cause output fluctuations in EH-IES energy supply equipment, posing significant threats to system stability. To address these challenges, a multi-objective bi-layer EH-IES planning model considering energy storage system is established, aiming at optimizing both economic performance and stability. This model employs non-dominated sorting genetic algorithm II (NSGA II) to optimally plans the capacity and location of EH-IES's equipment under 13-node district heating network (DHN), IEEE-33, and IEEE-69 node test systems. Simulation results show that DHN's thermal customer satisfaction is improved by 77.19 % (7.076 °C), with the total cost is $234,310.09/day. For the distributed network (DN), the net load fluctuation is reduced by 1.8491 MW (23.38 %) and 2.6083 MW (26.16 %), and the voltage deviation is reduced by 0.3479 p.u. (44.23 %) and 1.7349 p.u. (61.89 %), with respective daily costs of $403.17 and $898.36. Consequently, the proposed method can improve the cost efficiency and sustainability of the system operation.