This paper investigates the magnetoresistance of micron-sized MnAs/GaAs(AlAs)/MnAs magnetic tunnel junctions. We measure an asymmetric bias dependence of the magnetoresistance in which the negative contribution is attributed to resonant tunneling through a midgap defect band. Within this model we find a spin polarization of 60% for MnAs at the interface with GaAs. Moreover, we show that spin-dependent tunneling is a powerful technique for spectroscopic measurements of defects in a very thin layer.