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This paper proposes an algorithm for the recognition and separation of speech signals in non-stationary noise, such as another speaker. We present a method to combine hidden Markov models (HMMs) trained for the speech and noise into a factorial HMM to model the mixture signal. Robustness is obtained by separating the speech and noise signals in a feature domain, which discards unnecessary information. We use mel-cepstral coefficients (MFCCs) as features, and estimate the distribution of mixture MFCCs from the distributions of the target speech and noise. A decoding algorithm is proposed for finding the state transition paths and estimating gains for the speech and noise from a mixture signal. Simulations were carried out using speech material where two speakers were mixed at various levels, and even for high noise level (9 dB above the speech level), the method produced relatively good (60% word recognition accuracy) results. Audio demonstrations are available at www.cs.tut.fi/~tuomasv.