The creation and interaction of dark solitons in a two-component Bose-Einst
ein condensate is investigated. For a miscible case, the interaction of dar
k solitons in different components is studied. Various possible scenarios a
re presented, including the formation of a soliton-soliton bound pair. We a
lso analyze the soliton propagation in the presence of domains, and show th
at a dark soliton can be transferred from one component to the other at the
domain wall when it exceeds a critical velocity. For lower velocities mult
iple reflections within the domain are observed, where the soliton is evapo
rated and accelerated after each reflection until it finally escapes from t
he domain.