AbstractVesicles are versatile drug delivery systems and a fundamental chassis from which to build synthetic cells. Multivesicular structures, composed of multiple lipid‐bound compartments, could form systems with complex functionalities and recapitulate collective behaviour found in living tissues. However, control over number, composition, and arrangement of compartments within multivesicular structures has been limited. Here, we generate multivesicular structures composed of hundreds of lipid‐bound compartments arranged in precisely controlled geometries. Through a dewetting process, we transfer 3D‐printed droplet networks from oil to aqueous phase and obtain multivesicular structures with designed, complex architectures stable for weeks. We encapsulate membraneless coacervate sub‐compartments within the lipid‐bound compartments of the 3D‐printed multivesicular structures. Further, we use the multivesicular structures as a platform to build synthetic tissues that interact with the external aqueous environment by releasing or sensing molecules and ions. Finally, we build synthetic tissues that synthesize proteins encoded by encapsulated genes.