A numerical study predicts that a single metamolecule with magnetism and chirality has giant magnetochiral (MCh) effects at microwave frequencies. The magnetism is provided by the ferromagnetic resonance of ferrite under dc bias magnetic fields, while the chirality is provided by the spiral arrangement of dielectric cubes with Mie resonance. The dielectric and magnetic resonances interfere in the metamolecule, resulting in a two-order of magnitude enhancement of the MCh effect compared with that reported in previous studies. This prediction is verified experimentally. A unity-order directional difference in the refractive index caused by the MCh effect is also demonstrated. This study is a significant milestone in the practical use of the MCh effect.