We present a theory for phase-separated liquid coacervates with salt, taking into account spatial heterogeneities and interfacial profiles. We find that charged layers of alternating sign can form around the interface while the bulk phases remain approximately charge neutral. We show that the salt concentration regulates the number of layers and the amplitude of the layer's charge density and electrostatic potential. Such charged layers can either repel or attract single-charged molecules diffusing across the interface. Our theory could be relevant for artificial systems and biomolecular condensates in cells. Our work suggests that interfaces of biomolecular condensates could mediate charge-specific transport similar to membrane-bound compartments.