We report on theoretical investigations and k.p calculations of carrier tunneling, both electrons and holes, in model systems and heterostructures composed of exchange-split III-V semiconductors, involving spin-orbit interactions. The two media are separated-or not-by a thin tunnel barrier made out of a (III-V) semiconductor. In a 2x2 exchange-split band model, we show that, when Dresselhaus interactions are included in the conduction band of two exchange-split semiconductors in contact in the antiparallel states of magnetization, the electrons are differently transmitted with respect to an axis orthogonal to both normal axis of the interface and of the magnetization. The transmission asymmetry (A) between +k// and -k// incidence is shown to be maximal (A=100%) at some points of the Brillouin zone corresponding to a totally quenched transmission at some given incidence angles. More generally, we derive a universal character of the transmission asymmetry A vs. the in-plane incidence wavevector, the reduced kinetic energy and exchange parameter, A being universally scaled by a unique function, independent of the spin-orbit strength and of material parameters. This particular asymmetry feature is reproduced by a more complete 14x14 band model involving coupling with the conduction band. On the other hand, calculations performed in the valence-band of equivalent model heterostructures and including tunnel barriers in both 6x6 (without inversion) and 14x14 k.p band model more astonishingly highlight, the same trends in the transmission asymmetry (A) which is related to the difference of orbital chirality and to the related branching (overlap) of the corresponding evanescent wavefunctions responsible for tunneling current. In both cases of electrons and holes, the asymmetry appears to be robust and persists only when a single electrode is magnetic.