We report the magnetization reversal and magnetic anisotropy behavior of ultrathin Co/Cu(111)/Co (dCu=20 and 27 Å) trilayer structures prepared by MBE on a 500-Å Ge/GaAs(110) epilayer. We describe an arrangement in which the magnetization components parallel and perpendicular to the applied field are both determined from longitudinal MOKE measurements. For the samples examined, coherent rotation of the magnetization vector is observed when the magnetic field is applied along the hard in-plane anisotropy axis, with the magnitude of the magnetization vector constant and close to its bulk value. Results of micromagnetic calculations closely reproduce the observed parallel and perpendicular magnetization loops, and yield strong uniaxial magnetic anisotropies in both layers while the interlayer coupling appears to be absent or negligible in comparison with the anisotropy strengths. An absence of antiferromagnetic (AF) coupling has been observed previously [W. F. Egelhoff, Jr. and M. T. Kief, Phys. Rev. B 45, 7795 (1992)] in contrast to recent results, indicating that AF coupling [M. T. Johnson et al., Phys. Rev. Lett. 69, 969 (1992)] and GMR [D. Grieg et al., J. Magn. Magn. Mater. 110, L239 (1992)] can occur in Co/Cu(111)/Co structures grown by MBE, but these properties are sensitively dependent on growth conditions. The absence of coupling in our samples is attributed to the presence of a significant interface roughness induced by the Ge epilayer. The uniaxial anisotropies are assumed to arise from strain or defects induced in the film.