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Dispersion features of both bulk and surface polaritons propagating through a magnetic-semiconductor superlattice influenced by an external static magnetic field are studied. The dispersion relations are derived in a general form assuming an arbitrary direction of magnetization with respect to wave propagation. It has been shown that providing a conscious choice of the constitutive parameters and material fractions of both magnetic and semiconductor layers of the superlattice, a number of phenomena, like bulk and surface polaritons passband splitting, anomalous dispersion, crossing and anti-crossing effects in dispersion characteristics, and coexistence of surface polaritons within the bulk polariton continua can be achieved