This isn't an inane lyric, just logic-defying. From the refrain of The Seven Joys of Mary:

... and blesséd may he be
Both Father, Son, and Holy Ghost ...

"Both"? When citing the Trinity?

But there it is, in black-&-white, right there in the Oxford Book of Carols. Think June & Maddy sang it that way too though I can't remember. (Have to confess, I've changed it to "praise".) Lovely song, though -