I think the two-planes solution will work.  If you watch a real fog-bank closely, you'll see that everything appears to be either in or out of the layers.  For objects on the scale of cars or trees, there isn't a visible 'in-between'.  I suppose the in-between-ness *might* show on something like a very long warehouse that runs parallel to the road.

If you want the fog to be 'lifting' so it's stronger above, you can use the V variable to control the strength of the plane's transparency.

The power function makes it possible to shape the up-down fade better.

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