This dissertation presents a study on heterogeneous network structure in two distinct classes of soft material systems: disordered assemblies of jammed binary spheres and ordered morphologies of block copolymer melts. The aim is to investigate the combined role of geometry and entropy in structure formation of soft matter assemblies. First, we investigate the influence of particle size asymmetry on structural properties of jammed binary sphere mixtures. We give evidence of two distinct classes of materials separated by a critical size ratio that marks the onset of a sharp transition due to simultaneous jamming of a sub-component of the packing. We give a heuristic, geometric argument to understand this transition and its impact on the particle network connectivity. We then present a simple and efficient numerical tool to characterize the network morphologies of block copolymers. We apply our algorithm to extract and compare the network geometry from experimental and theoretical double gyroid morphologies. Finally, we examine the influence of mesoscale geometry on polymer segment orientation at much smaller length scales. We demonstrate that underlying the well-known composition profiles are generic, heterogeneous segment orientation textures that couple strongly to the morphology. We give evidence that confinement of polymer chains in mesochiral domains induces segment scale chirality in the melts.