We present a computational study of the adhesive and structural properties of the Al/Al2O3 interfaces as building blocks of the metal-insulator-metal (MIM) tunnel devices, where electron transport is accomplished via tunneling mechanism through the sandwiched insulating barrier. The main goal of this paper is to understand, on the atomic scale, the role of the geometrical details in the formation of the tunnel barrier profiles. Initially, we concentrate on the adhesive properties of the interfaces. To provide reliable results, we carefully assess the accuracy of the traditional methods used to examine Al/Al2O3 systems. These are the most widely employed exchange-correlation functionals—local-density approximation and two different generalized gradient approximations; the universal binding-energy relation for predicting equilibrium interfacial distances and adhesion energies; and the ideal work of separation as a measure of junction stability. In addition, we show that the established interpretation of the computed ideal work of separation might be misleading in predicting the optimal interface structures. Finally, we perform a detailed analysis of the atomic and interplanar relaxations in each junction, and identify their contributions to the tunnel barrier parameters. Our results imply that the structural irregularities on the surface of the Al film have a significant contribution to lowering the tunnel barrier height, while atomic relaxations at the interface and interplanar relaxations in Al2O3 may considerably change the width of the barrier and, thus, distort its uniformity. Both the effects may critically influence the performance of the MIM tunnel devices.