In this paper, we investigate delay-optimized edge caching in the integrated satellite-terrestrial network with diverse content popularity distribution and user access modes. Based on the cooperation among the base stations, the satellite and the gateway, we propose a three-layer caching architecture to provide content service for both base station access users and satellite access users. Considering diverse content preferences for users in different areas, we formulate the content placement problem with the objective to minimize the average content retrieving delay of the network. By introducing the concept of the delay reduction gain and the caching benefit, we first derive the optimal caching strategy for base stations in different areas separately. Then, we propose two algorithms to calculate the cooperative caching strategy of the network, in which reduced search space is applied based on theoretical analysis. While the dynamic programming algorithm can achieve the optimal solution of the content placement problem, the submodular optimization based algorithm can provide guaranteed performance with relatively low complexity. Simulation results show that the proposed caching strategies can effectively improve the network delay performance.