Sleep problems constitute a significant public health problem due to their high prevalence and impact on mental health and health behaviours, with major consequences for individuals and society. Therefore, the aim of this study was to investigate the association between sleep problems (duration and quality), mental health and health behaviours. Cross-sectional data was derived from the 2021 health survey 'How are you?' from the Central Denmark Region. The study population was a stratified random sample of 33,925 respondents aged 16 years or older. We used logistic regression models to analyse the associations between sleep problems and indicators of mental health and health behaviour. The models were adjusted for sex, age, educational attainment, labour market attachment, cohabitation, and indicators of mental health and health behaviour. A prevalence of around 10% for both short- and long sleep duration and poor sleep quality was found. All were associated with poor mental health-related quality of life, depression, stress, perceived stressors and obesity. In addition, short sleep duration was associated with daily smoking, and long sleep duration was associated with physical inactivity and daily smoking. Our findings revealed a stronger association between sleep problems and mental health indicators in comparison to health behaviours. We found that sleep duration and sleep quality in broad terms were associated with similar variables within mental health and health behaviour. These findings underline the importance of adopting a comprehensive approach to addressing sleep problems in the context of health promotion, disease prevention, treatment and rehabilitation.