In this paper, we propose transceiver design strategies for the two-cell multiple-input multiple-output (MIMO) interfering broadcast channel where inter-cell interference (ICI) exists in addition to inter-user interference (IUI). We first formulate the generalized zero-forcing interference alignment (ZF-IA) method based on the alignment of IUI and ICI in multi-dimensional subspace. We then devise a minimum weighted-mean-square-error (WMSE) method based on "regularizing" the precoders and decoders of the generalized ZF-IA scheme. In contrast to the existing weighted-sum-rate-maximizing transceiver, our method does not require an iterative calculation of the optimal weights. Because of this, the proposed scheme, while not designed specially to maximize the sum-rate, is computationally efficient and achieves a faster convergence compared to the known weighed-sum-rate maximizing scheme. Through analysis and simulation, we show the effectiveness of the proposed regularized ZF-IA scheme.