The magnetic properties of antiferromagnetic (AFM) spins were investigated using x-ray magnetic linear dichroism (XMLD) in epitaxial NiO/CoO/MgO(001) films as a function of film thickness, temperature, and interface modulation. We found that the NiO AFM spins undergo a spin reorientation transition (SRT) from the in-plane orientation to the out-of-plane orientation at a critical NiO thickness. The NiO AFM SRT can be attributed to the competition between the out-of-plane anisotropy of the NiO AFM spins and the AFM interfacial exchange coupling with the CoO in-plane spins. The NiO SRT thickness increases with the CoO thickness and also with the interfacial coupling strength. The temperature-dependent XMLD measurement indicates that the exchange coupling at the NiO/CoO interface can greatly enhance the Néel temperature of the CoO layer.