We consider a two-way full-duplex (FD) multiple-input multiple-output (MIMO) communication system in which devices are equipped both with multi-tap analog interference cancellers and TX-RX beamforming capabilities, and propose a joint analog and digital algorithm to simultaneously maximize the rate and minimize the self-interference (SI) in such a system. The MMSE-based joint design framework of TX- RX beamforming and SI cancellation scheme proposed relies only on a simple iterative procedure performed with quantities evaluated via closed form expressions for the MMSE scaling factor and the beamforming matrix here derived. Simulation results demonstrate that the proposed scheme is capable of suppressing residual interference down to background noise levels typical of wireless systems, significantly outperforming similar methods previously proposed.