Chemical systems may be maintained far from equilibrium by sequestering otherwise reactive species into different microenvironments. It remains a significant challenge to control the amount of chemical energy stored in such systems and to utilize it on demand to perform useful work. Here, we show that redox-active molecules compartmentalized in multiphasic structured-liquid devices can be charged and discharged to power a load on an external circuit. The two liquid phases of these devices feature charge-complementary polyelectrolytes that serve a dual purpose: they generate an ionically conductive coacervate membrane at the liquid-liquid interface, providing structural support; they also mitigate active-material crossover between phases via ion pairing with the oppositely charged anolyte and catholyte active materials. Structured-liquid batteries enabled by this design were rechargeable over hundreds of hours. We envision that these devices may be integrated with soft electronics to enable functional circuits for smart textiles, medical implants, and wearables.