By means of first-principles DFT computations, we systematically investigate the geometries, stabilities, electronic and magnetic properties of fully and partially hydrogenated zigzag BNC nanoribbons (fH-zBNCNRs and pH-zBNCNRs) with interfacial N–C or B–C connections. It is revealed that in the lowest-lying configuration of hybrid fH-zBNCNRs, the constituent C and BN segments can possess respective chair and boat conformations and both of them are connected by the chair mode, independent of the N–C/B–C interface. Changing the ribbon width and the ratio of BN to C can endow these fH-zBNCNR systems with abundant electronic and magnetic properties involving nonmagnetic (NM) semiconductivity, ferromagnetic (FM) metallicity, antiferromagnetic (AFM) metallicity as well as AFM half-metallicity. Besides, manipulating the hydrogenation pattern and ratio can also result in rich electronic and magnetic behaviors in pH-zBNCNRs, where NM semiconductivity, AFM semiconductivity, AFM metallicity and even AFM spin gapless semiconductor are observed. Additionally, the origin of the magnetism in these hydrogenated zBNCNRs is analyzed in detail. Finally, all of these hydrogenated BNC structures can possess a favorable formation energy, large binding energy per hydrogen atom and high thermal stability, indicating the great possibility of their experimental realization by hydrogenating pristine zBNCNRs. These valuable insights can be advantageous for promoting hybrid BNC-based nanomaterials in the applications of spintronics and multifunctional nanodevices.