The degradation of hybrid perovskite films when exposed to the ambient air is a major challenge for the development of perovskite-based photovoltaics at large scale. At present, little is known about the environmental degradation of perovskite films associated with the development of structural defects or open volumes (such as, atomic vacancies, voids, crystallographic defects and grain boundary defects) in the lattice and about the depth dependence of the structural degradation. Therefore, in this work, we use Doppler broadening-positron annihilation spectroscopy (DB-PAS) depth-profiling to gain insight into the structural degradation of CH3NH3PbI3-xClx perovskite when exposed to ambient air. In parallel, we investigate the effect of ultrathin (<1 nm) atomic layer deposited (ALD) Al2O3 processed directly on top of the perovskite as a means to suppress the degradation process. Specifically, we infer that the perovskite degradation involves changes in open volumes in its crystal lattice. This could be caused by the ingress of H2O molecules into the cation vacancies. In parallel, chemical changes in the perovskite films upon decomposition are observed, accompanied by a decrease in the film thickness as a function of air exposure time. When the perovskite films are decorated with ALD Al2O3, the latter delays the thickness reduction of the perovskite layer during air exposure and also suppresses the changes in its open volumes and chemical transformations. Our findings illustrate that an improved understanding of the perovskite degradation process can be obtained using DB-PAS, especially when combined with other thin film characterization techniques, such as X-ray diffraction and X-ray photoelectron spectroscopy.