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In this paper we propose a novel iterative speech feature enhancement and recognition architecture for noisy speech recognition. It consists of model-based feature enhancement employing Switching Linear Dynamical Models (SLDM), a hidden Markov Model (HMM) decoder and a state mapper, which maps HMM to SLDM states. To consistently adhere to a Bayesian paradigm, posteriors are exchanged between these processing blocks. By introducing the feedback from the recognizer to the enhancement stage, enhancement can exploit both the SLDMs ability to model short-term dependencies and the HMMs ability to model long-term dependencies present in the speech data. Experiments have been conducted on the Aurora II database, which demonstrate that significant word accuracy improvements are obtained at low signal-to-noise ratios.