The preparation of high quality epitaxial heterointerfaces of lattice mismatched dissimilar materials is one of the challenging tasks for advanced semiconductor devices. We have used the concept of van der Waals epitaxy, namely the deposition of two-dimensional layered materials like GaSe onto properly terminated three-dimensional substrates to prepare new heterointerfaces on Si of different surface orientation. Film growth and properties were investigated in situ by low-energy electron diffraction (LEED) and soft X-ray photoemission (SXPS) using integrated UHV preparation and analysis chambers. On Si(111) a hexagonal GaSe epitaxial layer grows on top of a preformed Si-Ga-Se van der Waals-like termination layer. A distorted Si-Ga-Se layer is also formed on Si(110), which evidently leads to an hexagonal surface mesh as substrate for further growth of crystalline GaSe. On Si(100), two domains of azimuthally aligned GaSe(0001) films are deposited. The usually given constraints in lattice mismatch, and even of different surface symmetry, can evidently be overcome by the use of van der Waals-like surface termination layers of the substrates. Thus, novel device structures combining compound semiconductors with Si seem to be feasible.