The layered oxides being considered as intercalation compounds for lithium batteries display significant differences between the long-range crystal structure and local arrangements around individual atoms. These differences are important, because the local atomic environments affect Li-ion transport and, hence, the oxide's rate capability, by determining activation barrier energies, by blocking or opening Li-diffusion pathways, etc. Traditional diffraction methods provide key information on the average crystal structure. However, no single experimental technique can unequivocally determine the average long-range crystal structure and the distribution of local environments over crystallographic distances while retaining atomic-scale resolution. Therefore, in this study, we have employed a combination of diffraction, microscopy, and spectroscopy techniques to investigate the long-range (similar to 1 mu m) and local structure (<= 1 nm) of Li1.2Co0.4Mn0.4O2, which is a model compound for layered oxides being considered for transportation applications. We find that Li1.2Co0.4Mn0.4O2 contains mostly Mn4+ in Li2MnO3-like atomic environments and Co3+ in LiCoO2-like atomic environments, which are intimately mixed over length scales of >= 2-3 nm, resulting in a Li1.2Co0.4Mn0.4O2 crystallite composition that appears homogeneous over the long-range. In addition, we observed a quasi-random distribution of locally monoclinic structures, topotaxially integrated within a rhombohedral-NaFeO2 framework. Based on these observations, we propose a dendritic microstructure model for Li1.2Co0.4Mn0.4O2 consisting of well integrated LiCoO2- and Li2MnO3-like structures.