As devices are reduced in size, interfaces start to dominate electrical transport making it essential to be able to describe reliably how they transmit and reflect electrons. For a number of nearly perfectly lattice-matched materials, we calculate from first-principles the dependence of the interface transparency on the crystal orientation. Quite remarkably, the largest anisotropy is predicted for interfaces between the prototype free-electron materials silver and aluminium for which a massive factor of two difference between (111) and (001) interfaces is found.