Liquid-liquid phase separation at complex interfaces plays an important role in biological systems and material applications. A key question is to understand the effect of interfacial properties on the thermodynamics and dynamic pathways of liquid-liquid phase separation, which remains to be clarified. Here, we create double emulsion droplets and study the phase separation of immiscible polymer solutions at the water/oil/water interface. Various block copolymers are used to modulate the interfacial properties, which make phase separation configurable to eyeball-like, Janus double-shell, and inverse eyeball-like structures. The eyeball-like droplets are obtained through a one-step coalescence or spreading process, while the Janus double-shell and inverse eyeball-like structures are created by a two-step "coalescence-and-inverse spreading" or "spreading-and-inverse spreading" process. We reveal that the selection of a dynamic pathway is dependent on the polymer composition and interfacial properties. However, the equilibrium structures of phase separation are determined only by the interfacial properties of coexisting phases. Such phase behaviors are unique in contrast with the polymer phase separation on plane substrates and yet ubiquitous at double emulsion interfaces in more than ten different systems. The equilibrium structures and dynamic pathways are quantitatively explained by our analysis using normalized interfacial tension, which unifies all data on an equilibrium morphology diagram and a temporal evolution diagram, respectively. This study provides a method to understand phase separation behaviors at double emulsion interfaces and is also helpful for regulating particle configurations and membrane structures at liquid-liquid interfaces.