To combine the advantages of microstructural finite element (FE) models of asphalt composites and macrostructural FE models of pavement structures subjected to rolling tire load, this article introduces a novel consistent simulation chain. Starting with experimental tests of asphalt mortar, an existing microstructural FE model of a Stone Mastic Asphalt, which contains coarse aggregates, asphalt mortar and air voids, is parameterized and validated. The microstructural model is then applied to identify macroscopic (homogenized) material properties of the asphalt mixture that are used in FE computations of two pavement structures under rolling tire load. The macrostructural pavement computations are evaluated by a new macro–micro-interface that generates realistic time-dependent displacement boundary conditions representing the rolling tire loading conditions for the microstructural model. A verification and exemplary microstructural computations at rolling tire load boundary conditions show that the introduced simulation chain allows for the investigation of the processes, stresses, and strains inside the asphalt composite at realistic loading conditions. Results can, for example, be used to improve the experimental tests on the component level as well as to gain a better understanding of the interacting processes in asphalt mixtures under rolling tire load.