In this paper, we investigate an interference alignment (IA) technique introduced by Cadambe and Jafar in mutually interfering broadcast channels (IFBCs). First, we study the spatial multiplexing gain (SMG) for the 3-cell IFBC where all base stations and mobile users are equipped with multiple antennas. To achieve the derived optimal SMG, we extend the IA algorithm designed for K-user multi-input multi-output (MIMO) interference channels (IFCs) to the IFBC. In this paper, we present the IA scheme in conjunction with user selection which outperforms the time division multiple access (TDMA) technique in the IFBC environment. The optimal scheduling method capitalizes on multiuser diversity to achieve a significant fraction of sum capacity by using an exhaustive search algorithm. Since the computational complexity of the optimal scheduling method is prohibitive, a reduced complexity suboptimal scheduling method is proposed based on a coordinate ascent approach. Simulation results confirm that the reduced complexity scheduling algorithm achieves the sum rate close to the optimal algorithm with much reduced complexity.