We have investigated the exchange bias ͑EB͒ in ultrathin epitaxial Cr/Fe/Ag͑001͒ nanopatterned bilayers characterized by atomic-scale-tailored interfaces consisting of nanoripples aligned along the ͓100͔ Fe direction. Precisely measuring the magnetic anisotropy of the system, we quantitatively characterized the energetics of the magnetization reversal in terms of domain-wall propagation in the Fe layer and discussed the influence of the interface structure in determining the exchange bias and promoting the domain-wall processes. We found no influence of the relative orientation of the field-cooling direction with respect to the nanoripple orientation in determining the EB magnitude, but we observed that the anisotropic morphology generates characteristic spin frustrations affecting the energetics of different domain-wall processes.