We investigated the upper critical magnetic field H-c of a superconductor-ferromagnet (S/F) bilayer of Nb/Cu41Ni59 and a Nb film (as reference). We obtained the dependence of H-c perpendicular to and H-c parallel to (perpendicular and parallel to the film plane, respectively) on the temperature T by measurements of the resistive transitions and the dependence on the inclination angle theta of the applied field to the film plane, by nonresonant microwave absorption. Over a wide range, H-c perpendicular to and H-c parallel to show the temperature dependence predicted by the Ginzburg-Landau theory. At low temperatures and close to the critical temperature, deviations are observed. While H-c (theta) of the Nb film follows the Tinkham prediction for thin superconducting films, the Nb/Cu41Ni59-bilayer data exhibit deviations when theta approaches zero. We attribute this finding to the additional anisotropy induced by the quasi-one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state and propose a new vortex structure in S/F bilayers, adopting the segmentation approach from high-temperature superconductors.