Network science constitutes now a fundamental framework for studying complex systems and modeling the ever-growing data deluge that occurs in virtually all fields of knowledge. Over the last decade, multilayer networks contributed to revolutionize the study of systems characterized by multiple scales or levels i.e. layers of interactions. These models shed a new light on interconnected systems by ex- hibiting unexpected topological correlations, robustness and synchronization properties, just to name a few. Historically multilayer networks leveraged their comparative advantages over classical networks, focusing on the interactions of nodes both within and between layers. Although recent studies started to characterize layer properties per se, layer characterization and its interplay with the classical node characterization still remain to be explored. In this manuscript, we propose the node-layer duality, a unifying framework to study the structural properties of nodes and layers. We show that both node and layer properties provide complementary information when considering the second moment (i.e. variance) of their distribution. We extensively study these complementarity by deriving a stochastic rewiring model that selectively rewires links according to either node, or layer or both dimensions. Using this rewiring approach, we analytically derive and numerically validate a formal duality relationship between the node and layer dimensions. In particular, we derive and validate a closed-form of this relationship in the case of random multiplex and multilayer networks. Based on local connectivity, we show that the complementarity of the node-layer duality clusters real- world multiplex networks coming from different contexts (social, biological, infrastructure...) into networks that have a spatial connotation and others that do not have one. Moreover, we provide a method to efficiently visualise the connectivity of multiplex networks in the node and layer dimensions. In this effort to characterize real-world systems, we focus our analysis on multilayer brain networks. The brain is perhaps the most striking example of complex systems that has benefited from the multi- layer thrust. Actually the brain at the large-scale can be recorded using many neuroimaging technics (MRI,EEG,MEG,fMRI...) and its functional properties can be investigated along different modes (temporal, frequential). The properties of these brain networks are fundamental to uncover the normal brain functioning as well as new effective biomarkers to prevent, track or even cure brain diseases. In particular, cross-frequency coupling (CFC) i.e. interactions between different brain frequencies has been shown to be a major component of information transfer within the brain across spatiotemporal scales. Although modeling CFC was already suggested to better characterize diseases, multilayer brain networks that integrate CFC are still relatively unexplored. In parallel, the frequency-based multilayer networks (i.e. layers representing the frequency of brain activity) showed promising results in characterizing Alzheimer’s disease. Therefore, we apply the node-layer duality framework to characterize simultaneously the regions (nodes) and frequencies (layers) of multi-frequency brain networks including CFC. Based on the correlation between local and global measures of connectivity and cognitive decline, we find that Alzheimer’s disease seems to be characterized not only by the disruption of connectivity in specific brain regions, but more importantly by the aberrant coordination between frequencies. In particular, we recover the importance of the connectivity disruption in the alpha band (8-13 Hz) which is a well-kown feature of Alzheimer’s disease. We conclude on the opportunity of systematically adopting a dual characterization in the study of the structure of multilayer networks by exploiting its characteristics which are shared among duality relationships in general.