The mixing of tracers by mesoscale eddies, parameterized in many ocean general circulation models (OGCMs) as a diffusive-advective process, contributes significantly to the distribution of tracers in the ocean. In the ocean interior, diffusive contribution occurs mostly along the direction parallel to local neutral density surfaces. However, near the surface of the ocean, small-scale turbulence and the presence of the boundary itself break this constraint and the mesoscale transport occurs mostly along a plane parallel to the ocean surface (horizontal). Although this process is easily represented in OGCMs with geopotential vertical coordinates, the representation is more challenging in OGCMs that use a general vertical coordinate, where surfaces can be tilted with respect to the horizontal. We propose a method for representing the diffusive horizontal mesoscale fluxes within the surface boundary layer of general vertical coordinate OGCMs. The method relies on regridding/remapping techniques to represent tracers in a geopotential grid. Horizontal fluxes are calculated on this grid and then remapped back to the native grid, where fluxes are applied. The algorithm is implemented in an ocean model and tested in idealized and realistic settings. Horizontal diffusion can account for up to 10\% of the total northward heat transport in the Southern Ocean and Western boundary current regions of the Northern Hemisphere. It also reduces the vertical stratification of the upper ocean, which results in an overall deepening of the surface boundary layer depth. Lastly, enabling horizontal diffusion leads to meaningful reductions in the near-surface global bias of potential temperature and salinity.