In this paper, we provide a precise expression of the spatial multiplexing gain (SMG) for two mutually interfering multiple-input multiple-output (MIMO) broadcast channels using linear transceiver, referred to as MIMO-IBC. The MIMO-IBC has two base stations and K1, K2 users, each equipped with multiple antennas, where independent messages are transmitted over fixed channels. We observe the variation of the SMG with respect to user antenna distribution, and compare the derived result to the SMG of the interference channel with full cooperation among users. Additionally, we propose a linear precoding and decoding scheme for the MIMO-IBC in terms of maximizing the total sum rate, by extending one designed for single-cell multiple-input single-output broadcast channels. Simulation results confirm the accuracy of our theoretical SMG analysis for the MIMO-IBC.