The aim of the study was to produce biocomposites based on chitosan and sodium hyaluronate hydrogels supplemented with bioglasses obtained under different conditions (temperature, time) and to perform an in vitro evaluation of their cytocompatibility using both indirect and direct methods. Furthermore, the release of ions from the composites and the microstructure of the biocomposites before and after incubation in simulated body fluid were assessed. Tests on extracts from bioglasses and hydrogel biocomposites were performed on A549 epithelial cells, while MG63 osteoblast-like cells were tested in direct contact with the developed biomaterials. The immune response induced by the biomaterials was also evaluated. The experiments were carried out on both unstimulated and lipopolysaccharide (LPS) endotoxin-stimulated human peripheral blood cells in the presence of extracts of the biocomposites and their components. Extracts of the materials produced do not exhibit toxic effects on A549 cells, and do not increase the production of proinflammatory cytokines tumour necrosis factor alpha (TNF-α) and interleukin (IL-6) by blood cells in vitro. In direct contact with MG63 osteoblast-like cells, biocomposites containing the reference bioglass and those containing SrO are more cytocompatible than biocomposites with ZnO-doped bioglass. Using two testing approaches, the effects both of the potentially toxic agents released and of the surface of the tested materials on the cell condition were assessed. The results pave the way for the development of highly porous hydrogel-bioglass composite scaffolds for bone tissue engineering.