The objective of this study was to produce an innovative bigel formulation by combining glycerol monostearate (GMS) oleogel with hydrogels stabilized by various agents, including cold pressed chia seed oil by-product gum (CSG), gelatin (G), and whey protein concentrate (WPC). The findings indicated that the choice of hydrogel influenced the rheological, textural, and microstructural properties of the bigels. The G′ value of the bigel samples was higher than G″, indicating that all the bigels exhibited solid-like characteristics. In order to numerically compare the dynamic rheological properties of the samples, K′ and K″ values were calculated using the power law model. K′ values of the samples were found to be higher than K″ values. The K′ value of bigel samples was significantly affected by the hydrogel (HG)/oleogel ratio (OG) and the type of stabilizing agent used in the hydrogel formulation. As the OG ratio of bigel samples increased, the K′ value increased significantly (p < 0.05). The texture values of the samples were significantly affected by the HG/OG ratio (p < 0.05). The study’s findings demonstrated that utilizing CSG, G, and WPC at an OG ratio more than 50% can result in bigels with the appropriate hardness and solid character. The low-fat mayonnaise was produced by using these bigels. The low-fat mayonnaise showed shear-thinning and solid-like behavior with G′ values greater than the G″ values. Low-fat mayonnaise produced with CSG bigels (CSGBs) showed similar rheological properties to the full-fat mayonnaise. The results showed that CSG could be used in a bigel formulation as a plant-based gum and CSGB could be used as a fat replacer in low-fat mayonnaise formulation.