We consider the problem of unsupervised classification of hidden Markov models (HMC) with dependent noise. Time is discrete, the hidden process takes its values in a finite set of classes, while the observed process is continuous. We adopt an extended HMC model in which the rich possibilities of different kinds of dependence in the noise are modelled via copulas. A general model identification algorithm, in which different noise margins and copulas corresponding to different classes are selected in given families and estimated in an automated way, from the sole observed process, is proposed. The interest of the whole procedure is shown via experiments on simulated data and on a real SAR image.