Hidden Markov chains (HMCs) are widely used in unsupervised Bayesian hidden discrete data restoration. They are very robust and, in spite of their simplicity, they are sufficiently efficient in many cases. However, in complex situations, extensions of HMCs models are of interest. In particular, when sojourn time in hidden states is not geometrical, hidden semi-Markov chains (HSMCs) may work better. Besides, hidden evidential Markov chains (HEMCs) showed its interest in non-stationary situations. In this paper, we propose a new model simultaneously extending HSMCs and HEMCs. Based on triplet Markov chains (TMCs), it is used in an unsupervised framework, parameters being estimated with the Expectation-Maximization (EM) algorithm. We validate its interest through some experiments on hand-drawn images noised with artificial noises.