Leveraging the advantage of satellite and terrestrial networks, the integrated satellite terrestrial networks (ISTNs) can help to achieve seamless global access and eliminate the digital divide. However, the dense deployment and frequent handover of satellites aggravate intra- and inter-system interference, resulting in a decrease in downlink sum rate. To address this issue, we propose a coordinated intra- and inter-system interference management algorithm for ISTN. This algorithm coordinates multidimensional interference through a joint design of inter-satellite handover and resource allocation method. On the one hand, we take inter-system interference between low earth orbit (LEO) and geostationary orbit (GEO) satellites as a constraint, and reduce interference to GEO satellite ground stations (GEO-GS) while ensuring system capacity through inter-satellite handover. On the other hand, satellite and terrestrial resource allocation schemes are designed based on the matching idea, and channel gain and interference to other channels are considered during the matching process to coordinate co-channel interference. In order to avoid too many unnecessary handovers, we consider handover scenarios related to service capabilities and service time to determine the optimal handover target satellite. Numerical results show that the gap between the results on the system sum rate obtained by the proposed method and the upper bound is reduced as the user density increases, and the handover frequency can be significantly reduced.