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We study a non-Hermitian variant of the -dimensional Dirac wave equation that hosts a real energy spectrum with pairwise-orthogonal eigenstates. In the spatially uniform case, the Hamiltonian's non-Hermitian symmetries allow its eigenstates to be mapped to a pair of Hermitian Dirac subsystems. When a wave is transmitted across an interface between two spatially uniform domains with different parameters, an anomalous form of Klein tunneling occurs, whereby reflection is suppressed while the transmittance is substantially higher or lower than unity. The interface can even function as a simultaneous laser and coherent perfect absorber. Remarkably, the violation of flux conservation occurs entirely at the interface, with no wave amplification or damping taking place in the bulk. Moreover, at energies within the Dirac mass gaps, the interface can support exponentially localized boundary states with real …