In this paper, we lay an analytic framework for computing the downlink success probability of cellular networks, taking into account a frequency reuse distance as an interference mitigation scheme. We model the frequency reuse distance using tools from stochastic geometry, namely, we utilize the Matérn hard-core (MHC) point process to capture the effect of interference protection zones created around base stations. To model the overall cellular network, we introduce a new point process composed of N superimposed MHC processes, where each individual MHC process corresponds to a co-channel base station group; this new point process is called the union- MHC (UMHC) process. We further investigate the resulting performance of the UMHC process and present the link success probability in integral form. The success probability can be evaluated for an arbitrary fading model and an arbitrary number of orthogonal resource groups. We test the newly proposed model against the practical data sets from a network operator and observe a good match of the results.