During the last decade, it has been well understood that communication over multiple antennas can increase linearly the multiplexing capacity gain and provide large spectral efficiency improvements. However, the majority of studies in this area were carried out ignoring cochannel interference. Only a small number of investigations have considered cochannel interference, but even therein simple channel models were employed, assuming identically distributed fading coefficients. In this paper, a generic model for a multiantenna channel is presented incorporating four impairments, namely additive white Gaussian noise, flat fading, path loss and cochannel interference. Both point-to-point and multiple-access MIMO channels are considered, including the case of cooperating Base Station clusters. The asymptotic capacity limit of this channel is calculated based on an asymptotic free probability approach which exploits the additive and multiplicative free convolution in the R- and S-transform domains, respectively, as well as properties of the η and Stieltjes transform. Numerical results are utilized to verify the accuracy of the derived closed-form expressions and evaluate the effect of the cochannel interference.