Materials that can mimic the fibrillar architecture of native extracellular matrix (ECM) while allowing for independent regulation of viscoelastic properties may serve as ideal, artificial ECM (aECM) to regulate cell functions. Here we describe an interpenetrating network of click-functionalized alginate, crosslinked with a combination of ionic and covalent crosslinking, and fibrillar collagen type I. Varying the mode and magnitude of crosslinking enables tunable stiffness and viscoelasticity, while altering neither the hydrogel’s microscale architecture nor diffusional transport of molecules with molecular weight relevant to typical nutrients. Further, appropriately timing sequential ionic and covalent crosslinking permits self-assembly of collagen into fibrillar structures within the network. Culture of human mesenchymal stem cells (MSCs) in this mechanically-tunable ECM system revealed that MSC expression of immunomodulatory markers is differentially impacted by the viscoelasticity and stiffness of the matrix. Together, these results describe and validate a novel material system for investigating how viscoelastic mechanical properties of ECM regulate cellular behavior.