Personal electronic devices including smartphones give access to behavioural signals that can be used to learn about the characteristics and preferences of individuals. In this study, we explore the connection between demographic and psychological attributes and the digital behavioural records, for a cohort of 7,633 people, closely representative of the US population with respect to gender, age, geographical distribution, education, and income. Along with the demographic data, we collected self-reported assessments on validated psychometric questionnaires for moral traits and basic human values and combined this information with passively collected multi-modal digital data from web browsing behaviour and smartphone usage. A machine learning framework was then designed to infer both the demographic and psychological attributes from the behavioural data. In a cross-validated setting, our models predicted demographic attributes with good accuracy as measured by the weighted AUROC score (Area Under the Receiver Operating Characteristic), but were less performant for the moral traits and human values. These results call for further investigation since they are still far from unveiling individuals' psychological fabric. This connection, along with the most predictive features that we provide for each attribute, might prove useful for designing personalised services, communication strategies, and interventions, and can be used to sketch a portrait of people with a similar worldview.