Simple and effective imaging strategies are of utmost interest for applications on a lab-on-chip scale. In fact, the majority of diagnostic tools for medical as well as biotechnological studies still employ image-based approaches. Having onboard the chip a compact but powerful imaging apparatus with multiple imaging capabilities, such as 3D dynamic focusing along the optical axis, unlimited field of view (FoV) and double outputs, namely, intensity and quantitative phase-contrast maps of biological objects, is of extreme importance for the next generation of Lab-on-a-Chip (LoC) devices. Here we present a coherent 3D microscopy approach with a holographic modality that is specifically suitable for studying biological samples while they simply flow along microfluidic paths. The LoC device is equipped with a compact linear array detector to capture and generate a new conceptual type of a digital hologram in the space-time domain, named here as Space-Time Digital Hologram (STDH). The reported results show that the method is a promising diagnostic tool for optofluidic investigations of biological specimens.