The preparation and properties of novel edible bigel systems based on olive oil oleogels structured with 15% monoglycerides and different hydrogels formed with 8, 10 or 12% gelatin or gelatin plus 1% κ-carrageenan were studied. The effect of hydrogel composition and oleogel/hydrogel ratio on physicochemical characteristics and microstructure, as well as mechanical and thermal properties of the resultant bigels was examined. An increased proportion of oleogel led to a decrease in hardness (10.34–43.95 N) and an increase in the cohesiveness of bigels (0.13–0.36). Addition of κ-carrageenan to the bigel system increased hardness (25.47–89.00 N) and decreased cohesiveness (0.12–0.16). Microscopy revealed the formation of an oleogel-in-hydrogel bigel system with significantly smaller oil droplets when only gelatin was used as a hydrogelator. Bigels containing gelatin and κ-carrageenan had the lowest swelling capacity, possibly due to formation of hydrogen bonds and electrostatic interactions between gelatin and κ-carrageenan resulting in an inelastic structure that could not absorb water. Differential scanning calorimetry revealed an increase in the melting enthalpy of the monoglycerides from 5.35 mJ/mg to 8.85 mJ/mg with increasing oleogel proportion in bigels, while the incorporation of κ-carrageenan improved the thermal stability of the biphasic system. Fourier transform infrared spectroscopy documented the existence of a complex between gelatin and κ-carrageenan and confirmed that the mechanism of bigels formation is based on the physical interactions of the two structured phases. These results provide a comprehensive overview regarding the structure and functional properties of bigels with potential applications in foods.