The growth of ultrathin perylene films on Cu(110) and Cu(100) surfaces has been studied by means of He atom scattering, low-energy electron diffraction, scanning tunneling microscopy, thermal desorption spectroscopy, and X-ray photoelectron spectroscopy with a special emphasis on the interface structure. In addition to several ordered submonolayer phases, two distinctly different monolayer structures were found at substrate temperatures below 380 K and at about 450 K on Cu(110). The rather open saturation structure formed at elevated temperatures reveals an enhanced density of substrate steps, which indicates an adsorption-induced modification of the Cu(110) surface. In contrast to that, on Cu(100), only a close-packed c(8 x 4) monolayer structure is formed without any less-dense-packed structures.