This paper introduces a new method for multichannel speech enhancement based on a versatile modeling of the residual noise spec-trogram. Such a model has already been presented before in the single channel case where the noise component is assumed to follow an alpha-stable distribution for each time-frequency bin, whereas the speech spec-trogram, supposed to be more regular, is modeled as Gaussian. In this paper, we describe a multichannel extension of this model, as well as a Monte Carlo Expectation-Maximisation algorithm for parameter estimation. In particular, a multichannel extension of the Itakura-Saito nonnegative matrix factorization is exploited to estimate the spectral parameters for speech, and a Metropolis-Hastings algorithm is proposed to estimate the noise contribution. We evaluate the proposed method in a challenging multichannel denoising application and compare it to other state-of-the-art algorithms.