This paper presents a Bayesian framework for under-determined audio source separation in multichannel reverberant mixtures. We model the source signals as Student's t latent random variables in a time-frequency domain. The specific structure of musical signals in this domain is exploited by means of a non-negative matrix factorization model. Conversely, we design the mixing model in the time domain. In addition to leading to an exact representation of the convolutive mixing process, this approach allows us to develop simple probabilistic priors for the mixing filters. Indeed, as those filters correspond to room responses they exhibit a simple characteristic structure in the time domain that can be used to guide their estimation. We also rely on the Student's t distribution for modeling the impulse response of the mixing filters. From this model, we develop a variational inference algorithm in order to perform source separation. The experimental evaluation demonstrates the potential of this approach for separating multichannel reverberant mixtures.