We report the application of nanoindentation and atomic force microscopy to establish the fundamental relationships between mechanical properties and chemical bonding in a dense inorganic-organic framework material: Ce(C2O4)(HCO2), 1. Compound 1 is a mixed-ligand 3-D hybrid which crystallizes in an orthorhombic space group, in which its three basic building blocks, i.e. the inorganic metal-oxygen-metal (M-O-M) chains and the two organic bridging ligands, (oxalate and formate) are all oriented perpendicular to one another. This unique architecture enabled us to decouple the elastic and plastic mechanical responses along the three primary axes of a single crystal to understand the contribution associated with stiff vs compliant basic building blocks. The (001)oriented facet that features rigid oxalate ligands down the c-axis exhibits the highest stiffness and hardness (E similar to 78 GPa and H similar to 4.6 GPa). In contrast, the (010)-oriented facet was found to be the most compliant and soft (E similar to 43 GPa and H similar to 3.9 GPa), since the formate ligand, which is the more compliant building block within this framework, constitutes the primary linkages down the b-axis. Notably, intermediate stiffness and hardness (E similar to 52 GPa and H similar to 4.1 GPa) were measured I on the (100)-oriented planes. This can be attributed to the Ce-O-Ce chains that zigzag down the a-axis (Ce center dot center dot center dot Ce metal centers form an angle of similar to 132 degrees) and also the fact that the 9-coordinated CeO9 polyhedra are expected to be geometrically more compliant. Our results present the first conclusive evidence that the crystal orientation dominated by inorganic chains is not necessarily more robust from the mechanical properties standpoint. Rigid organic bridging ligands (such as oxalate), on the other hand, can be used to produce greater stiffness and hardness properties in a chosen crystallographic orientation. This study demonstrates that there exists a vast opportunity to design the mechanical properties of dense hybrid framework materials through the incorporation of organic multifunctional ligands of varying rigidity.