The impact of interference is one of the most capacity limiting factors in cellular networks today. In order to host more users in existing systems and maximize the capacity of future networks, the use of interference suppression techniques are instrumental. In this paper, we propose a structured semi-blind parameter estimation procedure to support rejection, of unknown cochannel interference (CCI) in systems facing multipath channels with non-negligible delay spread. Employing spatio-temporal processing, the proposed scheme exploits the temporal correlation present in the output signal from an antenna array and the training data of a desired user in order to find parameter estimates that fit the range space of a structured CCI model to the signal subspace of the interfering signals. Simulation results illustrating the behavior of a spatio-temporal receiver using the proposed scheme with respect to both signal-to-noise and signal-to-interference ratios (SNRs and SIRs) are presented. In addition, results highlighting the impact of the training sequence length as well as the impact of the channel model order of the CCI users are also included.