This paper presents a study on applying satellite Interferometric Synthetic Aperture Radar (InSAR) technology for the remote monitoring of road bridges and interpreting the results from a structural standpoint. The motivation behind this study arises from the widespread deterioration observed in many road bridges worldwide, leading to the need for large-scale, economic, and effective structural health monitoring (SHM) techniques. While traditional contact-type sensors have cost sustainability limitations, remote sensing techniques, including satellite-based InSAR, offer interesting alternative solutions. The objective of this study is three-fold: (i) to process InSAR data specifically for road bridges in operational conditions through the Multi-Temporal InSAR technique and extract displacement time series of reflective targets on their decks; (ii) to interpret the observed millimetric bridge displacements to verify the consistency with expected response to environmental loads and the possibility to detect unexpected behaviours; and (iii) to investigate the correlation between bridge displacements and environmental loads as temperature and river water flow variations. The study focuses on the multi-span prestressed concrete A22 Po River Bridge in Italy, utilising a dataset of X-Band HIMAGE mode Stripmap images acquired over eight years by the satellite constellation COSMO-SkyMed. The study demonstrates the effectiveness of InSAR-based SHM in detecting temperature-induced displacements and identifying different bridge spans simply by studying the sign of the correlation between displacements and temperature variation. It also reveals an unexpected behaviour in a portion of the bridge retrofitted to prevent scour issues a few years before the dataset start date. Furthermore, the correlation between pier displacements and river level variations underscores the importance of considering environmental factors and the geotechnical characteristics of the foundation soils in bridge monitoring. The results obtained from this study are significant with a view to using this satellite InSAR-based monitoring for early detection of anomalous bridge behaviour on a large scale.