Two-tier overlay networks that consist of a conventional macrocell network and femtocell hotspots offer an economical solution for high user capacity and extended coverage. However, wireless interference across tiers causes significant performance degradation and restricts spectrum reuse. In this paper, we explore schemes to mitigate cross-tier interference with beamforming antennas for overlay networks. In our model, femtocells can operate with frequency spectrum that is either shared with or separated from the macrocell. The enhanced SIR from beamforming contributes to the population of femtocells with the shared spectrum, and thus improve the spectrum efficiency. Given a required SIR level, we show that which femtocells can use the shared spectrum and how much spectrum can be shared to maximize total utility.We show through a numerical performance evaluation that proposed schemes improve spectrum utilization for two-tier overlay networks.