The name Witherspoon does not appear to be on the document, though I've not transcribed all the names of the privates. Thomas Spight was the commanding. For anyone who might be interested, below is my attempt to transcribe some of what appears to be the most important parts of the document. I've reached out to the MS archives, but have not yet received a response.

Side 1:
Muster Roll, Company H, 24th Regiment, Mississippi - Volunteer, April 26, 1865
Colonel: R.W. Williamson
Captain: Thomas Spight
Also noted: (appears to be penned by the same hand)
M. Allen 1st Lieutenant
J.M Rutherford 2
L.P. Gray 1st Sergeant
R.A. Henry 2
W.J.B. Paieo (??) 3
G(?). K. Kisby (?) 4
Jns. H. Bilbs (?) 1st corp
W.L. Ceddiso (?) 2
J.S. Alexander Musician
…and then there are 31 additional names of those who seem to be Privates.

SIDE 2:
Station: Jamestown?
Signed by: Cpt. Spight, Commanding
and (illegible name, starting with a "B"), title: Special Commifermear?? (Commissioner?)
Remarks: Greensboro, N.C. May 1, 1865
In accordance with the terms of a Military Convention earlier(?)…..? on the 26th day of April, 1865 between General Joseph E. Johnston, Commanding Confederate army and Major General W.T. Sherman commanding United States Army in North Carolina, the officers and men whose names are bound(?) on this note(?) have given their solemn obligation not to take up arms against the government of the United States, until properly released from the obligation to return to their home not to be disturbed by the armided(?Armied? Armored?) state authorities, so long as they observe this obligation and obey the laws in force where they may reside(?).