A Regulation Doublet is basically a Prince Charlie with Argyle cuffs and Inverness flaps round the bottom instead of tails. (The name "doublet" is a bit of a misnomer here, but it has stuck over time.) Like a Prince Charlie, it comes with matching waistcoat. As thescot suggested, it could be worn with a white waistcoat (and bow tie) for white tie functions. I suppose you could do that with a Prince Charlie as well. A Regulation Doublet is not what bandsmen wear.