Femtocell and fractional frequency reuse (FFR) techniques have received wide attention as the solutions to the data surge problem in mobile networks. With FFR, the frequency band of a macrocell is divided into several frequency partitions (FPs), and the transmission power levels assigned to FPs differ from each other. In this paper, we propose a downlink resource partitioning scheme for two-tier networks, where macrocells adopting FFR are overlaid with the femtocells. With the proposed scheme, every FP is divided into the macro-dedicated, the shared, and the femto-dedicated portions. The ratio of these three portions is different for each FP. We suggest a method to determine a proper ratio of portions in each FP by using an optimization approach. Simulation results show that the proposed scheme maximizes the whole system capacity while satisfying the constraints on the minimum capacity requirement for both macrocell and femtocell.