Current regenerative strategies used for cartilage repair rely on biomaterial functionality as a scaffold for cells that may have potential in chondrogenic differentiation. The purpose of the research was to investigate the biocompatibility of enzymatically treated alginate/chitosan hydrosol sponges and their suitability to support chondrogenic differentiation of human adipose derived multipotent stromal cells (hASCs). The alginate/chitosan and enzyme/alginate/chitosan sponges were formed from hydrosols with various proportions and were used as a biomaterial in this study. Sponges were tested for porosity and wettability. The porosity of each sponge was higher than 80%. An equal dose of alginate and chitosan in the composition of sponges improved their swelling ability. It was found that equal concentrations of alginate and chitosan in hydrosols sponges assure high biocompatibility properties that may be further improved by enzymatic treatment. Importantly, the high biocompatibility of these biomaterials turned out to be crucial in the context of hydrosols’ pro-chondrogenic function. After exposure to the chondrogenic conditions, the hASCs in N/A/C and L/A/C sponges formed well developed nodules and revealed increased expression of collagen type II, aggrecan and decreased expression of collagen type I. Moreover, in these cultures, the reactive oxygen species level was lowered while superoxide dismutase activity increased. Based on the obtained results, we conclude that N/A/C and L/A/C sponges may have prospective application as hASCs carriers for cartilage repair.