Three bimetallic Cu–Ni nanoparticle-supported catalysts were synthesized by co-immobilization followed by H2 reduction. A chromium(III) terephthalate metal organic framework (MIL-101), titanium dioxide (TiO2), and carbon (C) with different properties (acidity and Brunauer–Emmett–Teller surface area) were selected as supports for studying the effect of the support nature on the catalytic activity and selectivity in the oxidation of benzyl alcohol. The physicochemical properties of the Cu–Ni-supported catalysts were characterized by XRD, NH3-TPD, nitrogen adsorption/desorption, TEM, EDS, XPS, and ICP-OES. Bimetallic Cu–Ni nanoparticles were highly dispersed on the support. The catalytic activities of CuNi/MIL-101, CuNi/TiO2, and CuNi/C were tested in the selective oxidation of benzyl alcohol to benzaldehyde in the presence of molecular oxygen under mild reaction conditions. The highest benzaldehyde yields were achieved with CuNi/TiO2, CuNi/MIL-101, and CuNi/C catalysts at 100 °C within 4 h under 5, 3, and 3 bar of O2, respectively. The bimetallic Cu–Ni-supported catalysts possessed two types of catalytic active sites: acid sites and bimetallic Cu–Ni nanoparticles. The CuNi/MIL-101 catalyst possessed a high number of acid sites and exhibited high yield during selective benzyl alcohol oxidation to benzaldehyde. Importantly, the catalysts exhibited a high functional group (electron-donating and electron-withdrawing groups) tolerance. Cu–Ni-supported catalysts with an Cu:Ni mole ratio of 1:1 exhibited the highest yield of 47% for the selective oxidation of benzyl alcohol to benzaldehyde. Reusability and leaching experiment results exhibited that CuNi/MIL-101 showed better stability than CuNi/TiO2 and CuNi/C catalysts due to the large porous cavities of MIL-101 support; these cavities can be used to trap bimetallic Cu–Ni nanoparticles and inhibit nanoparticle leaching.