There are numerous different hybrid models combining the HMM and a continuous model. As HMMs have been used most extensively in speech recognition, most of the hybrids have also been created for that purpose. Trentin and Gori  present a survey of speech recognition systems combining the HMM with some neural network model. These models are motivated by the end result of recognising speech by finding the correct HMM state sequence for the sequence of uttered phonemes. This is certainly one worthy goal but a good switching SSM can also be very useful in other time series modelling tasks.
The basic idea of all the hybrids is to use the SSM or another continuous dynamical model to describe the short-term dynamics of the data while the HMM describes longer-term changes. In speech modelling, for instance, the HMM would govern the desired sequence of phonemes while the SSM models the actual production of the sound, the dynamics of the mouth, the vocal cord etc.
The models presented here can be divided into two classes. First there are the true switching SSMs, i.e. combinations of the HMM and a linear SSM. The second class consists of models that combine the HMM with another dynamical model which is a continuous one but not a true SSM.