Polarization dependent x-ray photoemission electron microscopy was used to investigate the spin structure near the surface of an antiferromagnetic NiO(001) single crystal in response to the deposition of a thin ferromagnetic Co film. For the cleaved NiO surface we observe only a subset of bulklike antiferromagnetic domains which is attributed to minimization of dipolar energies. Upon Co deposition a spin reorientation near the NiO interface occurs, with the antiferromagnetic spins rotating in plane, parallel to the spins of the Co layer. Our results demonstrate that the spin configuration in an antiferromagnet near its interface with a ferromagnet may significantly deviate from that in the bulk antiferromagnet.