In this paper, we present a model for average rate analysis in a D2D communication overlaying two-tier downlink cellular network. Each mobile UE is able to establish D2D link with adjacent UEs or connect to a nearby macro or pico base station. Stochastic geometry analysis is adopted to characterize the medium contentions within macro and pico cells, as well as the D2D pair distributions, based on which closed-form per user average rate is derived with a careful consideration of the important issues such as frequency allocation, UE density, content hit rate, and cell coverage radius. Our results show that even for the overlaying case, D2D communication can significantly improve the per user average rate. Another finding is that the frequency allocation for D2D pairs should be carefully tuned according to network settings, which may result in totally different varying behaviors for the per user average rate.