I looked into this issue and a.) Even if you have an underlay turned on in your view the Grid lines are going to print solid black if that is what their Object Style is set. Even if I turn off the Grid annotation in my view with Hide Annotation in View, all of the occurences of that Grid line, including the underlayed Grid line are turned off.
The problem has to lay elsewhere. Check to see it your Object Style for Grid heads are set to Grey line color. Also make sure your propertiy type for Grids is set to black and solid. This will at least make the grid lines crossing the walls or other objects not appear as grey on top.
As far as I can observe Grid lines are intended to be on top of other objects. So it does not matter which order you draw Grid lines and other objects, and there is no control to have grid lines placed above or below.
Even if you import the Grids from one Revit project file into another they still are on top of the model elements.
It is the way things are.
Mel Persin, AIA