Structures and energetics of various, plausible realizations of the Al2O3(0001)Cu(111) interface have been studied by density-functional theory. The oxygen-terminated interface is found to be relatively strong with a work of separation (W-sep) of 7.03 J/m(2). For hydrogen-rich (e.g., moist) conditions, we have determined that the interface accommodates about 113 of a monolayer of hydrogen. This lowers W-sep to 4.72 J/m(2), which is, however, greater than the corresponding value for bulk copper, which implies that fracture in such a system occurs in the copper region, consistent with fracture toughness experiments. We also have studied the initial stages of copper and aluminum growth on the hydrogen-stabilized oxygen terminated Al2O3(0001) surface. Although a monolayer of aluminum already completely dissociates the interfacial O-H group, a monolayer of copper leaves it intact. If, for a thick copper film, such a full hydrogen layer were maintained, the resulting metastable interface would be very weak, with W-sep = 0.63 J/m(2).