We present linear transmit-receive filter design strategies for the two-cell multiple-input multiple-output (MIMO) interfering broadcast channel (IBC) where inter-cell interference (ICI) exists in addition to inter-user interference (IUI) within the cell. We first formulate a generalized zero-forcing interference alignment (ZF-IA) method capable of handling multiple data streams for each user. We proceed to further adjust the transmit-receive filters based on the minimum weighted-mean-square-error (WMSE) principle using the weights obtained from the initial generalized ZF-IA design, in an effort to to enhance the sum-rate performance. In contrast to the existing weighted-sum-rate-maximizing scheme, our method does not require an iterative calculation of the weights. Because of this, the proposed scheme, while not designed specifically to maximize the sum-rate, is computationally efficient and delivers favorable tradeoffs between performance and information exchange overhead.