Understanding properties of polymer alloys with computer simulations frequently requires equilibration of samples comprised of microscopically described long molecules. We present the extension of an efficient hierarchical backmapping strategy, initially developed for homopolymer melts, to equilibrate high-molecular-weight binary blends. These mixtures present significant interest for practical applications and fundamental polymer physics. In our approach, the blend is coarse-grained into models representing polymers as chains of soft blobs. Each blob stands for a subchain with N b microscopic monomers. A hierarchy of blob-based models with different resolution is obtained by varying N b. First the model with the largest N b is used to obtain an equilibrated blend. This configuration is sequentially fine-grained, reinserting at each step the degrees of freedom of the next in the hierarchy blob-based model. Once the blob-based description is sufficiently detailed, the microscopic monomers are reinserted. The hard excluded volume is recovered through a push-off procedure and the sample is re-equilibrated with molecular dynamics (MD), requiring relaxation on the order of the entanglement time. For the initial method development we focus on miscible blends described on microscopic level through a generic bead-spring model, which reproduces hard excluded volume, strong covalent bonds, and realistic liquid density. The blended homopolymers are symmetric with respect to molecular architecture and liquid structure. To parameterize the blob-based models and validate equilibration of backmapped samples, we obtain reference data from independent hybrid simulations combining MD and identity exchange Monte Carlo moves, taking advantage of the symmetry of the blends. The potential of the backmapping strategy is demonstrated by equilibrating blend samples with different degree of miscibility, containing 500 chains with 1000 monomers each. Equilibration is verified by comparing chain conformations and liquid structure in backmapped blends with the reference data. Possible directions for further methodological developments are discussed.