Due to their limited resolution, numerical ocean models need to be interpreted as representing filtered or averaged equations. How to interpret models in terms of formally averaged equations, however, is not always clear, particularly in the case of hybrid or generalized vertical coordinate models. We derive the averaged hydrostatic Boussinesq equations in generalized vertical coordinates for an arbitrary thickness weighted-average. We then consider various special cases and discuss the extent to which the averaged equations are consistent with existing model formulations. As previously discussed, the momentum equations in existing depth-coordinate models are best interpreted as representing Eulerian averages (i.e., averages taken at fixed depth), while the tracer equations can be interpreted as either Eulerian or thickness-weighted isopycnal averages. Instead we find that no averaging is fully consistent with existing formulations of the parameterizations in semi-Lagrangian discretizations of generalized vertical coordinate ocean models. Perhaps the most natural interpretation of generalized vertical coordinate models is to assume that the average follows the model’s coordinate surfaces. However, the existing model formulations are generally not consistent with coordinate-following averages, which would require “coordinate-aware” parameterizations that can account for the changing nature of the eddy terms as the coordinate changes. Alternatively, the model variables can be interpreted as representing either Eulerian or (thickness-weighted) isopycnal averages, independent of the model coordinate that is being used for the numerical discretization. Existing parameterizations in generalized vertical coordinate models, however, are usually not fully consistent with either of these interpretations. We discuss what changes are needed to achieve consistency.