Magnetoresistive effects are usually invariant upon inversion of the
magnetization direction. In noncentrosymmetric conductors, however, nonlinear
resistive terms can give rise to a current dependence that is quadratic in the
applied voltage and linear in the magnetization. Here we demonstrate that such
conditions are realized in simple bilayer metal films where the spin-orbit
interaction and spin-dependent scattering couple the current-induced spin
accumulation to the electrical conductivity. We show that the longitudinal
resistance of Ta|Co and Pt|Co bilayers changes when reversing the polarity of
the current or the sign of the magnetization. This unidirectional
magnetoresistance scales linearly with current density and has opposite sign in
Ta and Pt, which we associate with the modification of the interface scattering
potential induced by the spin Hall effect in these materials. Our results
suggest a route to control the resistance and detect magnetization switching in
spintronic devices using a two-terminal geometry, which applies also to
heterostructures including topological insulators