Hi Paty
Trying changing the name of your elevation field from 'ELEV' to 'Elevation' and rerun the export. You should find each line is given a Z value in the CAD file.
To take this concept further, try the opposite and bring a CAD file into ArcMap. You will notice that Arcmap creates a series of fields such as 'Layer', 'Color' etc. If you examine these and take note of the values in them, you should be able to use them in reverse. E.g. create a field called 'Layer' in your GIS file, give it a value and the export to CAD process should pick up on that field and use them when creating the CAD file.
I use this when exporting contour files - I have a field that identifies which are the minor and major contours, then use that to populate a 'Layer' and 'Color' field so that in the exported CAD file they are on different layers and in different colors.
Hope that helps.
-Paul