As essential components of the natural environment, urban green and blue spaces (UGBSs) hold significant potential to enhance public health and wellbeing. However, existing research is limited in understanding the spatiotemporal heterogeneity and nonlinear relationships characterizing how built environment (BE) features of UGBSs influence public happiness. This study takes Nanjing, China as a case study. It integrates multisource data (e.g., social media text, remote-sensing imagery, POI data, land use, etc.) and employs machine learning techniques (including sentiment analysis and random forest), to investigate the nonlinear effects and spatiotemporal dynamics of UGBSs’ BE on public happiness. The results show that nonlinear relationships (e.g., S-shaped and inverted U-shaped) commonly exist between UGBSs’ BE indicators and happiness. The influence of UGBSs’ BE on happiness demonstrates significant spatiotemporal dynamics. Diversity and destination accessibility were dominant factors from 2021 to 2023, whereas the importance of the design and density dimensions increased substantially after 2023. The influence varied across UGBS types; except for the diversity dimension, the BE’s density, design, and destination accessibility were significantly associated with happiness across all UGBS types. The study offers empirical evidence to inform planning and management of UGBS infrastructure, with the aim to maximize public health benefits and foster healthy cities.