In this paper, minimum MSE based interference alignment (IA) algorithm is developed for the interfering broadcast channel (IBC), which models the multi-cell downlink system, underlying cognitive radio, device-to-device and other scenarios. The IA precoders and decoders are computed to minimize the MSE. Cascade design is used for IA precoder design, where the first component precoder is obtained by MSE minimization and the second component of the cascade precoder is computed using zero forcing to null the intra-group interference. The resultant design is iterated to obtain the optimal precoder-decoder for IA. In simulations, the algorithm is analyzed for convergence, SNR behavior, and precoder initialization sensitiveness. It can be seen that the sum rate of the algorithm is non-decreasing in each iteration and performs better than the least squares based IA algorithm for IBC.