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This paper presents a novel approach to robust estimation of linear prediction (LP) model parameters in the application of speech enhancement. The robustness stems from the use of prior knowledge on the clean speech and the interfering noise, which are represented by two separate codebooks of LP model parameters. We propose to model the temporal dependency between short-time model parameters with a composite hidden Markov model (HMM) that is constructed by combining the speech and the noise codebooks. Optimal speech model parameters are estimated from the HMM state sequence that best matches the input observation. To further improve the estimation accuracy, we propose to perform interpolation of multiple HMM state sequences such that the estimated speech parameters would not be limited by the codebook coverage. Experimental results demonstrate the benefits and effectiveness of temporal dependency modeling and states interpolation in improving the segmental signal-to-noise ratio, PESQ and spectral distortion of enhanced speech.