The extracellular microenvironment provides critical cues that guide tissue development, homeostasis, and pathology. Deciphering the individual roles of these cues in tissue function necessitates the development of physically tunable culture platforms, but current approaches to create such materials have produced scaffolds that either exhibit a limited mechanical range or are unable to recapitulate the fibrous nature of in vivo tissues. Here we report a novel interpenetrating network (IPN) of gelatin-methacrylate (gelMA) and collagen I that enables independent tuning of fiber density and scaffold stiffness across a physiologically-relevant range of shear moduli (2–12 kPa), while maintaining constant extracellular matrix content. This biomaterial system was applied to examine how changes in the physical microenvironment affect cell types associated with the tumor microenvironment. By increasing fiber density while maintaining constant stiffness, we found that MDA-MB-231 breast tumor cells required the presence of fibers to invade the surrounding matrix, while endothelial cells (ECs) did not. Meanwhile, increasing IPN stiffness independently of fiber content yielded decreased invasion and sprouting for both MDA-MB-231 cells and ECs. These results highlight the importance of decoupling features of the microenvironment to uncover their individual effects on cell behavior, in addition to demonstrating that individual cell types within a tissue may be differentially affected by the same changes in physical features. The mechanical range and fibrous nature of this tunable biomaterial platform enable mimicry of a wide variety of tissues, and may yield more precise identification of targets which may be exploited to develop interventions to control tissue function.