[Bi0.87SrO2]2[CoO2]1.82 (BSCO) is one of the best p-type thermoelectric oxides but its structural and electronic properties are still poorly understood. BSCO is a misfit-layered compound consisting of an incommensurate stacking of hexagonal CoO2 and double rock-salt BiSrO2 layers. Here we combine experimental and computational approaches to investigate its crystallographic and electronic structure as well as thermoelectric transport properties. Considering different approximations for the subsystems stacking, we present a structural model that agrees well with both bulk and atomic-scale experimental data. This model, which suggests a level of Bi deficiency in the rock-salt layers, is then used to discuss the material's electronic, magnetic, and transport properties. We show that Bi deficiency leads to a band gap opening and increases p-type electronic conductivity due to the formation of Co4+ species that serve as itinerant holes within the predominantly Co3+ framework of the CoO2 layer. We validate these predictions using electron energy loss spectroscopy in the scanning transmission electron microscope. The relationship between the hole-doping mechanism and the changes of the local structure (in particular the level of Bi deficiency) is evaluated. The reliability of the simulations is supported by the calculated temperature dependence of the Seebeck coefficient, in good agreement with experimental measurements.