The quality of solid-electrolyte-interphase (SEI) dictates the performances of most battery chemistries, especially lithium (Li)-metal, but its formation processes as well as evolution during battery operation remain little understood due to the lack of reliable in-operando characterization tools of sufficient spatial and temporal resolutions. Herein, we report an in-operando reflection interference microscope (RIM) that enables the real-time imaging of SEI during formation and evolution in state-of-the-art electrolyte based on LiPF6 dissolved in organic carbonates. By mapping the minimal and localized optical signals generated from interphasial events, RIM reveals with extremely high sensitivity that the stratified structure of SEI formed during four distinct steps, including the emergence of a permanent inner inorganic layer enriched in LiF, the transient assembly of an interfacial structure of an electrified double layer, and the consequent emergence of a temporary outer organic-rich layer, whose presence is reversible with electrochemical cycling. Comparing the morphologies of SEIs, we identify an inverse correlation between the thicknesses of two interphasial sub-components: the thicker the LiF-rich inner layer, the thinner the organic-rich outer layer, implying that the permanent inorganic-rich inner layer dictates the organic-rich outer layer formation and Li nucleation. We also find that trace presence of water (50 ppm) in the electrolyte induces a much thicker and higher quality LiF-rich layer and a much thinner organic-rich layer in SEI, which leads to less electrolyte consumption, and more uniform Li nucleation on the electrode surface. The real-time visualization of SEI dynamics achieved for the first time in this work provides a guideline for the rational design of interphases, a battery component that has been the least understood and most challenging barrier to developing electrolytes for future batteries.