The ongoing need for materials with difficult-to-combine properties has driven dramatic advancements in the field of bioinspired and biomimetic (nano)structures. These materials blend order and disorder, making their structures difficult to describe and, thus, reproduce. Their practical design involves the approximate replication of geometries found in biological tissues, aiming to achieve desired functionalities using a diverse array of human-made molecular and nanoscale components. Although this approach led to the successful development of numerous high-performance nanocomposites, the rapidly growing demand for better and better materials in energy, water, health and other technologies necessitates an accelerated design process, multidimensional property assessment and, thus, a shift towards quantitative biomimetics. In this Perspective, we approach the design of complex bioinspired materials from the standpoint of interfacial chemistry and physics. Analysing typical examples of biological composites and their successful replicates, we propose a framework based on Taylor series and property differentials that quantifies their interdependence. Five specific cases are considered for limiting their cross-products in Taylor expansions, including discontinuities of differentials at interfaces and multiple scales of organization. We also discuss how the integration of theory, simulations and machine learning is central to the development of quantitative biomimetics. This approach will enable the n-dimensional optimization of contrarian properties by leveraging materials with a high volumetric density of interfaces, graph theoretical description of complex structures and hierarchical multiscale architectures.