Alginate-based hydrogels are widely utilized for various applications, including enzyme immobilization and the development of drug delivery systems, owing to their advantageous characteristics, such as low toxicity, high availability and cost-effectiveness. However, the broad applicability of alginate hydrogels is hindered by their limited mechanical and chemical stability, as well as their poor permeability to hydrophobic molecules. In this study, we addressed the mechanical properties and chemical resistance of alginate hydrogels in a high-pKa environment by the copolymerization of alginate with polyvinyl alcohol (PVA). The addition of PVA resulted in a threefold improvement in the shear modulus of the copolymeric hydrogel, as well as enhanced chemical resistance to (S)-α-methylbenzylamine, a model molecule with a high pKa value. Furthermore, we addressed the permeability challenge by introducing a betaine-propylene glycol deep eutectic solvent (DES) into the PVA-alginate copolymer. This led to an increased permeability for ethyl 3-oxobutanoate, a model molecule used for bioreduction to chiral alcohols. Moreover, the addition of the DES resulted in a notable improvement of the shear modulus of the resulting hydrogel. This dual effect highlights the role of the DES in achieving the desired improvement of the hydrogel as an immobilization carrier.