A two-tier heterogeneous cellular network (HCN) with intra-tier and inter-tier dependence is studied. The macro cell deployment follows a Poisson point process (PPP) and two different clustered point processes are used to model the cache-enabled small cells. Under this model, we derive approximate expressions in terms of finite integrals for the average delivery rate considering inter-tier and intra-tier dependence. On top of the fact that cache size drastically improves the performance of small cells in terms of average delivery rate, we show that rate splitting of limited-backhaul induces non-linear performance variations, and therefore has to be adjusted for rate fairness among users of different tiers.