The application of liver organoids is very promising in the field of liver tissue engineering; however, it is still facing some limitations. One of the current major limitations is the matrix in which they are cultured. The mainly undefined and murine-originated tumor matrices derived from Engelbreth-Holm-Swarm (EHS) sarcoma, such as Matrigel, are still the standard culturing matrices for expansion and differentiation of organoids toward hepatocyte-like cells, which will obstruct its future clinical application potential. In this study, we exploited the use of newly developed highly defined hydrogels as potential matrices for the culture of liver organoids and compared them to Matrigel and two hydrogels that were already researched in the field of organoid research [i.e., polyisocyanopeptides, enriched with laminin-entactin complex (PIC-LEC) and gelatin methacryloyl (GelMA)]. The newly developed hydrogels are materials that have a physicochemical resemblance with native liver tissue. Norbornene-modified dextran cross-linked with thiolated gelatin (DexNB-GelSH) has a swelling ratio and macro- and microscale properties that highly mimic liver tissue. Norbornene-modified chondroitin sulfate cross-linked with thiolated gelatin (CSNB-GelSH) contains chondroitin sulfate, which is a glycosaminoglycan (GAG) that is present in the liver ECM. Furthermore, CSNB-GelSH hydrogels with different mechanical properties were evaluated. Bipotent intrahepatic cholangiocyte organoids (ICOs) were applied in this work and encapsulated in these materials. This research revealed that the newly developed materials outperformed Matrigel, PIC-LEC, and GelMA in the differentiation of ICOs toward hepatocyte-like cells. Furthermore, some trends indicate that an interplay of both the chemical composition and the mechanical properties has an influence on the relative expression of certain hepatocyte markers. Both DexNB-GelSH and CSNB-GelSH showed promising results for the expansion and differentiation of intrahepatic cholangiocyte organoids. The stiffest CSNB-GelSH hydrogel even significantly outperformed Matrigel based on ALB, BSEP, and CYP3A4 gene expression, being three important hepatocyte markers.