Self-assembled (0.65)BiFeO3-(0.35)CoFe2O4 (BFO-CFO) nanostructures were deposited on SrTiO3 (001) and (111) substrates by pulsed laser deposition at various temperatures from 500 to 800°C. The crystal phases and the lattice strain for the two different substrate orientations have been determined and compared. The films grow epitaxial on both substrates but separation of the spinel and perovskite crystallites, without parasitic phases, is only obtained for growth temperatures of around 600-650°C. The BFO crystallites are out-of-plane expanded on STO(001), whereas they are almost relaxed on (111). In contrast, CFO crystallites grow out-of-plane compressed on both substrates. The asymmetric behavior of the cell parameters of CFO and BFO is discussed on the basis of the role of the epitaxial stress caused by the substrate and the spinel-perovskite interfacial stress. It is concluded that interfacial stress dominates the elastic properties of CFO crystallites and thus it may play a fundamental on the interface magnetoelectric coupling in these nanocomposites.