Huygens' metasurfaces, typically designed using sub-wavelength unit cells, allow the arbitrary control of electromagnetic waves. Two well-known unit-cell topologies are the wire-loop and stacked-layer designs. The wire-loop unit cell utilizes a conductive wire and loop to control its electric and magnetic responses, while the stacked-layer unit cell utilizes cascaded impedance sheets. Due to their versatility, Huygens' metasurfaces have been used for numerous applications. One interesting application has been perfect or reflectionless wide-angle refraction. In recent years, it was shown that for perfect refraction, omega-bianisotropy was required in Huygens' metasurfaces. To realize omega-bianisotropic designs, asymmetric unit cells were proposed and demonstrated utilizing stacked-layer unit cells. However, an omega-bianisotropic wire-loop unit cell for modulated Huygens' metasurfaces has yet to be demonstrated. This article demonstrates the design, simulation results, and measurements of an omega-bianisotropic wire-loop Huygens' metasurface for reflectionless wide-angle refraction of 71.8 degrees at 20 GHz. The design and simulation results of both TE and TM transverse-electric (TE) and transverse-magnetic (TM) designs are presented. Additionally, an optimized TM metasurface is experimentally verified through a combination of quasi-optical and far-field measurements. The presented results demonstrate negligible reflections, high scattered refraction efficiency, and a 0.7 GHz bandwidth, which validates the wire-loop unit-cell topology for realizing omega-bianisotropic Huygens' metasurfaces.