Aqueous droplets in oil that are coated with lipid monolayers and joined through interface bilayers are useful for biophysical measurements on membrane proteins. Functional networks of droplets that can act as light sensors, batteries and electrical components can also be made by incorporating pumps, channels and pores into the bilayers. These networks of droplets mimic simple tissues, but so far have not been used in physiological environments because they have been constrained to a bulk oil phase. Here, we form structures called multisomes in which networks of aqueous droplets with defined compositions are encapsulated within small drops of oil in water. The encapsulated droplets adhere to one another and to the surface of the oil drop to form interface bilayers that allow them to communicate with each other and with the surrounding aqueous environment through membrane pores. The contents in the droplets can be released by changing the pH or temperature of the surrounding solution. The multicompartment framework of multisomes mimics a tissue and has potential applications in synthetic biology and medicine.