The formation of passivating films is a common aging phenomenon, for example in weathering of rocks, silicon, and metals. In many cases, a dual-layer structure with a dense inner and a porous outer layer emerges. However, the origin of this dual-layer growth is so far not fully understood. In this work, a continuum model is developed, which describes the morphology evolution of the solid-electrolyte interphase (SEI) in lithium-ion batteries. Transport through the SEI and a growth reaction governed by the SEI surface energies are modelled. In agreement with experiments, this theory predicts that SEI grows initially as a dense film and subsequently as a porous layer. This dynamic phase transition is driven by the slowing down of electron transport as the film thickens. Thereby, the model offers a universal explanation for the emergence of dual-layer structures in passivating films.