A shared-parameter approach for jointly modelling longitudinal and survival data is proposed. With respect to available approaches, it allows for time-varying random effects that affect both the longitudinal and the survival processes. The distribution of these random effects is modelled according to a continuous-time hidden Markov chain, so that latent transitions may occur at any time point. Our formulation allows for (i) informative drop-out with precise time-to-event outcomes, while existing approaches are all based on drop-out indicators at precise measurement times, a feature that is at the least discarding possibly valuable information and (ii) completely non-parametric treatment of unequally spaced intervals between consecutive measurement occasions (even not in the presence of drop-out). For maximum likelihood estimation we propose an algorithm based on coarsening. The resulting estimator is studied by simulation. The approach is illustrated by an application to data about patients suffering from mildly dilated cardiomyopathy.