A theory for jointly optimizing transmitter and receiver finite impulse response (FIR) multiple-input multiple-output (MIMO) filters is developed in the presence of near-end crosstalk and additive channel noise independent of the original signal. The transfer function of the channel is a known MIMO transfer function with finite memory. Near-end crosstalk is included through another MIMO transfer function. The channel input signal is assumed to be power constrained. For a given channel with a maximum allowable average input power, the transmitter and receiver FIR MIMO filters are jointly optimized such that the mean square error (MSE) between the desired and reconstructed signal is minimized. An iterative numerical optimization algorithm is proposed. When compared to the methods available in the literature, the proposed method yields better results due to the joint optimization of the transmitter-receiver pair and is applicable to a more general scenario that may include correlated sources and near-end crosstalk.