A pelham is a *single* leverage bit with a curb chain, ridden with two reins.
A double bridle actually has two separate bits, a snaffle, called a bridoon when it's part of a double, and a curb bit, called a weymouth (if I got that wrong, I hope a more knowledgable dressage rider will correct me) There are two reins, but there are actually two separate and distinct mouthpieces in the horse's mouth. It is required above a certain level in dressage (4th, I think.) It allows a great deal of finesse - for instance, you can influence collection with the curb while influencing direction with the snaffle. I have only ever seen them used on upper level dressage horses, but that doesn't mean someone isn't out there using them badly or incorrectly on other horses.
ETA: two reins does not equal a double. There are a bunch of leverage bits ridden with two reins: pelhams, three rings, elevators and some gags. Two *bits* = a double bridle.