Spatial variations in the spin-reorientation transition of an exchange-coupled Co-wedge/YIG (Y3Fe5O12) bilayer, from perpendicular to in-plane domain structure, was studied using magnetic force microscopy (MFM) and photo-emission electron microscopy (PEEM). Even though MFM measurements of the YIG film showed perpendicular stripe domains, it was not possible to unambiguously resolve the domain structure of only the top ferromagnetic metal layer because of complications arising from the stray fields of the much thicker YIG underlayer. Hence, using element-specific, X-ray magnetic circular dichroism (XMCD) of the transition metal L3,2 edges (Co and Fe, respectively) for magnetic contrast, PEEM measurements were carried out to resolve the domain structure of the individual Co and YIG layers. The two were identical up to a Co thickness of 4.5 nm, confirming that the Co layer was exchange coupled with the YIG underlayer; however, a transition of the Co domains, from perpendicular to in-plane, was observed at thickness of 4.5-6 nm. For thicker regions of the Co film (>6 nm), a sizeable portion of the Co layer showed in-plane domains; their spins were perpendicular to the domain walls of the stripe domains with Co XMCD values in the range of -5% to +5%-a value much smaller than that of the perpendicular domains