Liquid–liquid phase separation is ubiquitous throughout biology, physics, materials science, and everyday life. Controlling interfaces is essential for forming organelles in cells and developing new materials. Traditional control of fluid interfaces relies on chemistry and interface-modifying agents such as surfactants and detergents. By merging a binary phase separating polymer solution with a microtubule-based active fluid, we demonstrate that activity provides a handle for interface control. Spontaneous flows generated through the active phase drive giant interfacial fluctuations and ultimately their disintegration. Our results reveal a mechanical mechanism for tuning interfaces and droplets, generating conformations and morphologies inaccessible to conventional chemistry-based equilibrium techniques. We study the structure and dynamics of the interface separating a passive fluid from a microtubule-based active fluid. Turbulent-like active flows power giant interfacial fluctuations, which exhibit pronounced asymmetry between regions of positive and negative curvature. Experiments, numerical simulations, and theoretical arguments reveal how the interface breaks up the spatial symmetry of the fundamental bend instability to generate local vortical flows that lead to asymmetric interface fluctuations. The magnitude of interface deformations increases with activity: In the high activity limit, the interface self-folds invaginating passive droplets and generating a foam-like phase, where active fluid is perforated with passive droplets. These results demonstrate how active stresses control the structure, dynamics, and break-up of soft, deformable, and reconfigurable liquid–liquid interfaces.