We have experimentally and numerically studied the directional birefringence of X-band microwaves by magnetochiral (MCh) effects of a single metamolecule under dc magnetic fields at room temperature. Phase and amplitude transmission coefficients from top and bottom, i.e., S parameters of S21 and S12, are measured for the single metamolecule consisting of a copper chiral structure and ferrite cylinder in a waveguide. By applying a dc magnetic field, we observe a difference between S21 and S12, which is an emergence of the MCh effects with simultaneous space-inversion and time-reversal symmetry breaking. Numerical calculation based on a finite element method reproduces well the experimental results of the MCh effects. The MCh effect can be enhanced by using the magnetic resonance of the ferrite cylinder. Notably, numerical calculation predicts that the MCh effect is extremely enhanced by interacting magnetic resonance with a specific resonant structural optical activity, leading to a giant MCh effect. The giant MCh effect observed in the present study originates from the one-way transparency caused by the Fano resonance in the metamolecule.