Graphene-covered copper surfaces have been exposed to borazine, (BH)3(NH)3, with the resulting surfaces characterized by low-energy electron microscopy. Although the intent of the experiment was to form hexagonal boron nitride (h-BN) on top of the graphene, such layers were not obtained. Rather, in isolated surface areas, h-BN is found to form μm-size islands that substitute for the graphene. Additionally, over nearly the entire surface, the properties of the layer that was originally graphene is observed to change in a manner that is consistent with the formation of a mixed h-BN/graphene alloy, i.e., h-BNC alloy. Furthermore, following the deposition of the borazine, a small fraction of the surface is found to consist of bare copper, indicating etching of the overlying graphene. The inability to form h-BN layers on top of graphene is discussed in terms of the catalytic behavior of the underlying copper surface and the decomposition of the borazine on top of the graphene.