Hi Jamie. I'm not sure if I understand your question, but here's some info:
If the DWG file includes lightweight polylines to represent the contours, ArcMap reads the elevation of the pline as the z value. If you want that Z value as an attribute, you can copy the cad feature class to a geodatabase and then use the GP tool "Add XY" to add the x, y, z coordinates as attributes.
If the lightweight polylines don't have an elevation, but have text near the line that represents the elevation, you may be able to use a spatial join or geoprocessing tools to associate the text as an attribute of the contour line.
Hope this helps!