This paper deals with the statistical restoration of hidden discrete signals, extending the classical methodology based on hidden Markov chains. The aim is to take into account the hidden signal and complex relationships between the noises which can be from different parametric models, non-independent, and of class-varying nature. We discuss some possibilities of managing it using copulas. Further, we propose a parameter estimation method and apply resulting unsupervised restoration methods in variety of situations. It is also validated by experiments performed in supervised and unsupervised context