Sleep is a complex biological process regulated by networks of neurons and environmental factors. As one falls asleep, neurotransmitters from sleep-wake regulating neurones work in synergy to control the switching of different sleep states throughout the night. As sleep disorders or underlying neuropathology can manifest as irregular switching, analysing these patterns is crucial in sleep medicine and neuroscience. While hypnograms represent the switching of sleep states well, current analyses of hypnograms often rely on oversimplified temporal descriptive statistics (TDS, e.g., total time spent in a sleep state), which miss the opportunity to study the sleep state switching by overlooking the complex structures of hypnograms. In this paper, we propose analysing sleep hypnograms using a seven-state continuous-time Markov model (CTMM). This proposed model leverages the CTMM to depict the time-varying sleep-state transitions, and probes three types of insomnia by distinguishing three types of wake states. Fitting the proposed model to data from 2056 ageing adults in the Multi-Ethnic Study of Atherosclerosis (MESA) Sleep study, we profiled sleep architectures in this population and identified the various associations between the sleep state transitions and demographic factors and subjective sleep questions. Ageing, sex, and race all show distinctive patterns of sleep state transitions. Furthermore, we also found that the perception of insomnia and restless sleep are significantly associated with critical transitions in the sleep architecture. By incorporating three wake states in a continuous-time Markov model, our proposed method reveals interesting insights into the relationships between objective hypnogram data and subjective sleep quality assessments.