We demonstrate the influence of interfacial strain on the growth modes of Ag films on Al(111), despite the small magnitude of the lattice misfit in this system. The strain is relieved by the formation of stacking fault domains bounded by Shockley partial dislocations. The growth mode and the step roughness appear to be strongly connected. Growth is three-dimensional (3D) as long as the steps are straight, but switches to 2D at higher coverage when the steps become rough. Anisotropic strain relaxation and straight steps seem to be related. We also report related observations for Al deposited on Ag(100).