To investigate half-metallic exchange bias interfaces, magnetic structures at ferromagnetic (FM)/antiferromagnetic (AFM) interfaces in the zinc blende transition-metal chalcogenides, and with compensated and uncompensated AFM interfaces, were determined by the full-potential linearized augmented plane-wave method. With the uncompensated AFM interface, an antiparallel alignment of the Cr and Mn moments induces an excellent half-metallicity. More striking still, in the compensated AFM interface the Cr moments in the FM layer lie perpendicular to the Mn moments in the AFM layer but the Mn moments strongly cant to induce a net moment so as to retain the half-metallicity. These findings may offer a key ingredient for exchange biased spintronic devices with 100% spin polarization, having a unidirectional anisotropy to control and manipulate spins at the nanoscale.