Considering that the network utilization cost in peer-to-peer (P2P) integrated energy transactions often accounts for more than 25% of the transaction costs, which significantly impacts the transaction benefits for prosumers, a P2P transaction strategy for the integrated electricity-heat energy system, which accounts for the network utilization cost, is proposed. Electrical distances in transaction path for electrical energy, and thermal resistances and lengths of pipelines in transaction path for thermal energy, are modeled to calculate the network utilization cost for both electricity and heat networks. By using the reputation index to assess the willingness of both parties participating in transactions, the optimization problem of P2P energy transaction strategy is constructed. Furthermore, a distributed solution method based on alternating direction method of multipliers (ADMM) is proposed. A P2P integrated energy simulation system comprising a 15-node electrical grid and an 8-node thermal network is established and further extended to a 33-node electrical grid and a 23-node thermal network system to verify the effectiveness of the proposed method and its scalability in P2P energy trading. Simulation results show that electricity-heat integrated energy P2P transactions with considering the network utilization cost are helpful to reducing energy transaction costs, promoting local energy consumptions, and increasing social welfares.