Caching at network edges has attracted more and more research interests recently for the purpose of alleviating the network traffic pressure especially in backhaul links and improving user experience. We study Heterogeneous Cellular Caching Networks (HCCNs) consisting of macro cells in which N small cell base stations (SBSs) equipped with cache memory operate in conjunction with the macro cell base station (MBS). We provide closed-form expressions of the MBS and SBSs utilization factors and average user-experienced-delay in HCCNs with overlapping coverage regions, considering general traffic models for the request arrivals based on the Independent Reference Model (IRM) and renewal traffic models. Moreover, we propose a novel caching scheme in HCCNs, namely Cooperative Most Popular Caching (CMPC), which outperforms the existing schemes in terms of delay. Subsequently, we present the bandwidth assignment problem aiming to minimize the average user-experienced-delay under stability and cache size constraints in HCCNs with overlapping coverage regions and stochastic request arrivals. Finally, the analytic results are validated through numerical results and real trace-driven experiments.