Multistate models are widely used for analyzing longitudinal data on disease progression over time. Many diseases manifest differently and what appears to be a coherent collection of symptoms is often the expression of a variety of distinct disease subtypes, each with a different rate of onset of symptoms and progression. We propose a mixture hidden Markov model (MHMM), where the underlying process is characterized by a finite mixture of multiple Markov chains, one for each disease subtype, while the observation process contains states corresponding to the common symptomatic stages of these diseases. Information on type of disease is partially available and reflects the pathway through certain hidden states in the corresponding disease process, facilitating the estimation of parameters involved in the proposed models. The method is demonstrated on a dataset to model the development and progression of dementia caused by Alzheimer's disease and non-AD dementia.