Metropolis Monte Carlo NVT computer simulations of 50:50 mixtures of L/D = 5 hard spherocylinders (N-HSC = 510) and L/D = 0.12 hard cut spheres (N-CS = 510) have been performed. At the start of the simulation, the system is taken as a totally demixed state of Fun rods and pure plates. For a packing fraction of 44% the system is found to be a fully mixed isotropic state, while at 48% two ordered phases (one rich in rods and one rich in plates) are found to coexist. In this Letter we examine the stable foe interface between the two liquid crystalline phases paying special attention to the orientational order through the interface.