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The transparency of two-dimensional (2D) materials to intermolecular interactions of crystalline materials has been an unresolved topic. Here we report that remote atomic interaction through 2D materials is governed by the binding nature, that is, the polarity of atomic bonds, both in the underlying substrates and in 2D material interlayers. Although the potential field from covalent-bonded materials is screened by a monolayer of graphene, that from ionic-bonded materials is strong enough to penetrate through a few layers of graphene. Such field penetration is substantially attenuated by 2D hexagonal boron nitride, which itself has polarization in its atomic bonds. Based on the control of transparency, modulated by the nature of materials as well as interlayer thickness, various types of single-crystalline materials across the periodic table can be epitaxially grown on 2D material-coated substrates. The epitaxial films can subsequently be released as free-standing membranes, which provides unique opportunities for the heterointegration of arbitrary single-crystalline thin films in functional applications.