I recently read Marching Home: Union Veterans and Their Unending Civil War by Brian Matthew Jordan, which touches on this briefly but does provide some important context.

I assume you are specifically referring to the reunions held for major anniversaries of large battles, such as the famous 1913 gathering at Gettysburg for the 50th anniversary. In the book, Jordan points out that while the most famous images and stories are of the elderly veterans "re-enacting" scenes like Pickett's Charge but ending with handshakes and embraces, these are not accurate portraits of how Union and Confederate veterans interacted at these reunions and are more representative of how journalists--especially Northern journalists--wanted to convey a message of sectional reconciliation. The reality was that the two sides were still very much at odds. Confederate speakers who gave speeches extolling the virtues of their cause were met with vigorous counter-speeches by Union men. In fact, seven elderly veterans were hospitalized following a brawl that started when a Confederate veteran impugned Abraham Lincoln in the presence of some Union veterans. At the Vicksburg reunion that same year, a Union veteran pointedly refused to ride in a wagon of Confederate veterans, instead insisting on renting a taxi at his own expense rather than ride with men he saw as traitors.

To your point, prior to the 1913 Gettysburg reunion, many Confederate veterans wrote to the event organizers asking all manner of questions, including whether black Union veterans were going to be allowed to participate--the implication being that they did not want to see those black veterans at the reunion. Unfortunately, the author does not mention any cases where black veterans interacted with Confederate veterans.

As far as reunions solely of Union veterans, black veterans did participate. The largest fraternal organization for northern veterans, the Grand Army of the Republic, allowed black veterans to join and participate in all of their functions. It was also common for veterans' publications to acknowledge the contribution, sacrifice, and fighting ability of African-American soldiers; the author also states that while the north was still virulently racist the shared experience of fighting the Civil War generally allowed white Union veterans to see black veterans as brothers-in-arms and the abolition of slavery as one of the things that justified their sacrifices. Black veterans were celebrated especially as there were fewer and fewer Union veterans left. Alvin Smith was a local celebrity in Akron, Ohio as the city's last Civil War veteran; he had escaped from a Kentucky plantation (where he had been purchased for $765.50) in 1863 and then enlisted in the 27th US Colored Infantry. He was a consistent presence at Decoration/Memorial Day, Independence Day, and Armistice Day celebrations. The year after Smith died in 1948, at the final GAR reunion in 1949 one of the six attendees was 105-year-old Joseph Clovese who had escaped from a plantation and joined the Union Army during the Vicksburg Campaign and later served with the 63rd US Colored Infantry through the end of the war.

So while the book does not answer your question about black veterans interacting with Confederate veterans, it does demonstrate that black veterans were full participants in commemorations of the Union Army.

Source: Jordan, Brian Matthew, Marching Home: Union Veterans and Their Unending Civil War, New York, Liveright Publishing Corporation, 2014.