The technology of perovskite-based solar cells is evolving rapidly, reaching certified power conversion efficiency values now exceeding 20 %. One of the main drawbacks hindering progress in the field is the long-term stability of the cells: the mixed halide perovskites used in most devices are sensitive to humidity and degrade on a timescale varying from hours to weeks. The degradation mechanisms are poorly understood, but likely arise from combined physical and chemical modifications at the nanometer scale. The characterization of pristine and degraded materials is difficult owing to their complex chemical and physical structure and their relatively poor stability. In this work, we investigated the changes in local composition and morphology of a standard device after 2 months of air exposure in the dark, using scanning transmission electron microscopy (STEM) with nanometer resolution for imaging and analysis. Because of a state-of-the-art technique that combines STEM and energy dispersive X-ray spectroscopy (EDX), and the use of different decomposition algorithms for multivariate analysis, we highlighted the migration of elements across the interfaces between the layers comprising the device. We also noticed a morphological degradation of the hole-transporting layer (HTL), representing one of the main factors enabling the infiltration of moisture in the device, which results in reduced performance.