Recent advances in experimental techniques allow for the fabrication of hybrid structures. Here, we study the electronic and molecular adsorption properties of the graphene (G)/hexagonal boron nitride (h-BN)-MXenes (Mo2C) hybrid nanosheets. We use first-principles calculations to explore the structure and electronic properties of the hybrid structures of G-2H-Mo2C and h-BN-2H-Mo2C with two different oxygen terminations of the Mo2C surface. The embedding of G or h-BN patches creates structural defects at the patch-Mo2C border and adds new states in the vicinity of the Fermi energy. Since this can be utilized for molecular adsorption and/or sensing, we investigate the ability of the G-M-O1 and BN-M-O1 hybrid structures to adsorb twelve molecules. Generally, the adsorption on the hybrid systems is significantly higher than on the pristine systems, except for N2 and H2, which are weakly adsorbed on all systems. We find that OH, NO, NO2, and SO2 are chemisorbed on the hybrid systems. COOH may be chemisorbed, or it may dissociate depending on its location at the edge between the G/h-BN and the MXene. NH3 is chemisorbed/physisorbed on the BN/G-M-O1 systems. CO, H2S, CO2, and CH4 are physisorbed on the hybrid systems. Our results indicate that the studied hybrid systems can be used for molecular filtration/sensing and catalysis.