Speech intelligibility is often severely degraded among hearing impaired individuals in situations such as the cocktail party scenario. The performance of the current hearing aid technology has been observed to be limited in these scenarios. In this paper, we propose a binaural speech enhancement framework that takes into consideration the speech production model. The enhancement framework proposed here is based on the Kalman filter that allows us to take the speech production dynamics into account during the enhancement process. The usage of a Kalman filter requires the estimation of clean speech and noise short term predictor (STP) parameters, and the clean speech pitch parameters. In this work, a binaural codebook-based method is proposed for estimating the STP parameters, and a directional pitch estimator based on the harmonic model and maximum likelihood principle is used to estimate the pitch parameters. The proposed method for estimating the STP and pitch parameters jointly uses the information from left and right ears, leading to a more robust estimation of the filter parameters. Objective measures such as PESQ and STOI have been used to evaluate the enhancement framework in different acoustic scenarios representative of the cocktail party scenario. We have also conducted subjective listening tests on a set of nine normal hearing subjects, to evaluate the performance in terms of intelligibility and quality improvement. The listening tests show that the proposed algorithm, even with access to only a single channel noisy observation, significantly improves the overall speech quality, and the speech intelligibility by up to 15%.