Reasonable planning of equipment in electric-heat integrated energy systems (EHIES) can effectively improve both economic efficiency and operational stability. This paper proposes a multi-objective planning model for EHIES based on non-dominated sorting genetic algorithm III (NSGA-III), with planning cost, district heating network (DHN) node temperature fluctuation, and active distributed network (ADN) node voltage fluctuation as objective functions. A heat-determined electric dispatch method is employed to determine the output power of the coupling devices in EHIES. In addition, simulation experiments are designed using a 13-node DHN and the IEEE-33 standard test networks. The optimized EHIES configuration scheme is re-integrated into the simulation networks to verify its effectiveness in improving ADN load stability. Experimental results show that, compared with the initial state, the proposed configuration method reduces EHIES emission costs by 40.75%, DHN heating temperature fluctuations by 9.37%, and ADN voltage fluctuations by 53.34%.