  We study current fluctuations of a two-species asymmetric exclusion process,
known as the Arndt-Heinzel-Rittenberg model. For a step-Bernoulli initial
condition with finite number of particles, we provide an explicit multiple
integral expression for a certain joint current probability distribution. By
performing an asymptotic analysis we prove that the joint current distribution
is given by a product of a Gaussian and a GUE Tracy-Widom distribution in the
long time limit, as predicted by non-linear fluctuating hydrodynamics.
