The mechanical environment plays an important role in cell signaling and tissue homeostasis. Unraveling connections between externally applied loads and the cellular response is often confounded by extracellular matrix (ECM) heterogeneity. Image-based multiscale models provide a foundation for examining the fine details of tissue behavior, but they require validation at multiple scales. In this study, we developed a multiscale model that captured the anisotropy and heterogeneity of a cell-compacted collagen gel subjected to an off-axis hold mechanical test and subsequently to biaxial extension. In both the model and experiments, the ECM reorganized in a nonaffine and heterogeneous manner that depended on multiscale interactions between the fiber networks. Simulations predicted that tensile and compressive fiber forces were produced to accommodate macroscopic displacements. Fiber forces in the simulation ranged from -11.3 to 437.7 nN, with a significant fraction of fibers under compression (12.1% during off-axis stretch). The heterogeneous network restructuring predicted by the model serves as an example of how multiscale modeling techniques provide a theoretical framework for understanding relationships between ECM structure and tissue-level mechanical properties and how microscopic fiber rearrangements could lead to mechanotransductive cell signaling.