Unidirectional transmission in thin stacked hole arrays (SHAs), whose spatial inversion symmetry is broken by adding a dielectric grating at one of the interfaces, is theoretically predicted and experimentally validated in the millimeter-wave regime. It appears at a fixed nonzero angle of incidence due to hybridization of SHA resonances with diffraction effects. In contrast to the earlier suggested structures with the diffraction relevant unidirectional transmission mechanism, the nonsymmetric diode-like structure founded on the intrinsically subwavelength SHA, which supports left-handed propagation, is less than one wavelength thick.