We study the phase transition in which a superconductor/normal interface depins from a twinning plane in a type-I superconductor. This transition is a variant of the recently discovered interface delocalization or ''wetting'' transition in similar materials. We calculate the phase diagram of the depinning transition as a function of the twinning-plane transparency for electrons, and the local enhancement of superconductivity. We focus on the limit of strongly type-I materials, kappa --> 0, in which analytic results can be obtained. We further compute the interface potential V(l) and use that to calculate the displacement profile l(y) of the transition zone between a pinned and a depinned superconducting/normal interface in the vicinity of a twinning plane. In principle, the interface displacement profile can be probed experimentally by measuring the location of the jump in the magnetic induction between the superconducting and normal phases.