Solid electrolyte interphase (SEI), a thin layer that dynamically forms between active electrode and electrolyte during battery operation, critically governs the performance of rechargeable batteries1-5. An ideal SEI is expected to be electrically insulative to prevent persistently parasitic reactions between the electrode and the electrolyte, while ionically conductive to facilitate Faradaic reactions of the electrode1,2,6. However, the true nature of the electrical properties of an SEI layer remains hitherto unclear due to the lack of a direct characterization method, leaving a range of behaviors of rechargeable batteries unelucidated. Here, we use in-situ bias transmission electron microscopy, for the first time, to directly measure the electrical properties of SEIs formed on copper (Cu) and lithium (Li) substrates. Surprisingly, we discover that, in terms of electrical behavior, SEI is distinctively different from a typical electrical insulator as what has been widely, and up to date, assumed ever since the discovery of SEI; rather, SEI shows voltage-dependent differential conductance.