I've read about that incident from the Federal side a couple of times -- some of which say the Confederates started it, and a Federal band responded -- this is the first I've seen from the Confederates. One account ends something like, "If the river had not been between us, I believe both armies would have come together and embraced." Bands on both sides reportedly joined in the "finale" and both armies sang "Home Sweet Home" in chorus ("the hills rang with the sound.") I'll try to track down the accounts (mostly in regimental histories).
That time just after Fredericksburg, and before the "Mud March" was a special period. The Regimental History of the 21st Mass., speaks of that Christmas:
“December 24th. The 21st had another cold twenty-four hours tour of picket duty along the river. One interesting feature of it was in hearing and seeing the merry revelry with which the rebels celebrated the advent of Christmas; there was a great firing of guns among them, and lots of glorious camp-fires. Quite a number of Union troops, on invitation of the rebels, crossed the river on Christmas Eve, by the rocky ford just above Falmouth, and helped them celebrate. A few evenings afterwards some fifty rebels returned the visit, coming over at the same place, and were made prisoners by order of the Officer of the Day, who on making his rounds came upon them, smoking and joking around the fires with our pickets. However, as soon as it was known at headquarters that the rebels were returning a visit by invitation, they were sent back to their side of the river, and stringent orders against having any talk or intercourse between the men of the two armies were issued and enforced.”
Officers can be such spoil-sports.