We introduce a novel imaging modality, named Space-Time Scanning Interferometry (STSI), which synthesizes interferograms mapped in a hybrid space-time domain. A single linear sensor array is sufficient to build up synthetic interferograms with unlimited Field of View (FoV) along the scanning direction, reduced noise, and allowing quantitative phase retrieval. We applied the STSI method to in-flow on-chip microscopy of biological samples. Out-of-focus recordings are performed using a single line detector, in order to synthesize an unlimited FoV Space-Time Digital Hologram (STDH) yielding full-field, 3D information. Experimental proofs have been carried out to demonstrate the useful capability of STDH to overcome the trade-off existing between FoV and sample magnification, thus providing a high-throughput, label/free, quantitative, diagnostic tool to study biological elements onboard LoC platforms.