Most synthetic hydrogels are formed through radical polymerization to yield a homogenous covalent meshwork. In contrast, natural hydrogels form through mechanisms involving both covalent assembly and supramolecular interactions. In this communication, we expand the capabilities of covalent poly(ethylene glycol) (PEG) networks through co-assembly of supramolecular peptide nanofibers. Using a peptide hydrogelator derived from the tryptophan zipper (Trpzip) motif, we demonstrate how in situ formation of nanofiber networks can tune the stiffness of PEG-based hydrogels, while also imparting shear thinning, stress relaxation, and self-healing properties. The hybrid networks show enhanced toughness and durability under tension, providing scope for use in load bearing applications. A small quantity of Trpzip peptide renders the non-adhesive PEG network adhesive, supporting adipose derived stromal cell adhesion, elongation, and growth. The integration of supramolecular networks into covalent meshworks expands the versatility of these materials, opening up new avenues for applications in biotechnology and medicine.