Using density functional theory and the non-equilibrium Green's function technique, we performed theoretical investigations on the magnetic and quantum transport properties of benzene-vanadium-borazine mixed organic/inorganic ligand sandwich clusters. The calculated results show that these finite sandwich clusters coupled to Ni electrodes exhibit novel quantum transport properties such as half-metallicity, negative differential resistance and spin-reversal effect, and can be viewed as a new kind of spin filter. However, for the infinite molecular wire, the ground state was identified as a ferromagnetic semiconductor with high stability. These findings suggest that the mixed organic/inorganic ligand sandwich clusters and molecular wires are promising materials for application in molecular electronics and spintronics.