Ok, I didn't know about this until I ran across this clip earlier today.
The late Allen Ludden moonlighted, if ya will, during the early years of Password and recorded an album of standards. He and wife Betty White did a summer stock production of the film, "Bells Are Ringing", which movie mavens will associate with actress Judy Holliday.
However, this might be the only time that I know of that the Luddens sang together on television. The occasion was a guest appearance on Dinah! & Friends in the late 70's. Password either was off the air or soon to return as Password Plus. Dinah Shore, along with Hal Linden (Barney Miller) and his wife, are as enraptured as the audience as Allen & Betty sing "Just In Time":