The problem of a semi-infinite crack propagating steadily along the interface of a viscoelastic bimaterial composite is investigated. One of the constituents of the composite is a strip and the other is a dissimilar half-plane. The viscoelastic behavior of both materials is modeled as a standard solid. The crack is driven by an arbitrary traveling shear load applied to the crack faces, producing a state of antiplane strain (mode 3). The boundary value problem is reduced to a Wiener-Hopf equation and solved in closed form by means of Cauchy-type integrals. For the specific case of an exponentially decaying load, the expression for the stress intensity factor is derived and its behavior as a function of crack-tip speed for different material combinations is examined. For some limiting cases, the solution is seen to coincide with known results. The important problem of an elastic-viscoelastic composite is also considered.