I have scanned the Cedar Hill stones at Vicksburg and have not found a dual unit example.

Pre-World War I Era Headstones and Markers

“The inscription on the special style for Civil War Confederate is also limited. The Southern Cross of Honor is automatically inscribed at the top. The name is arched, followed by abbreviated military organization and dates of birth and death. No additional items can be inscribed.”
http://www.cem.va.gov/cem/hmm/pre_WWI_era.asp

……….

Here is an example of dual affiliation which you could possibly use in support of your two unit inscription.

See the image of Robert C. Williamson, U. S. Navy & U. S. Coast Guard @
http://www.va.gov/vaforms/va/pdf/VA40-1330.pdf

Also, further down under Inscription Information, Mandatory Items

More than one branch of service is permitted, subject to space availability.

….

You might inquire of your nearby Cemetery Management who have experience in filling out these applications. They may have experience in dual unit applications.