Spikeofsilver is quite correct in saying that there is no evidence that large mail garments were laced through with leather thongs as a strengther. This fallacy evolved primarily from the way mail was portrayed in certain historical statuary and other images. The texture of mail, consisting as it does of a very dense pattern of repeating rings, is extremely difficult to draw or render in stone. This led to the creation of artistic conventions for depicting mail which certain historians misinterpreted. One of these conventions was to depict rows of small semi-circles, a method which does resemble both mail and "banded mail".
There are a few examples of leather thongs being laced through mail. Some mail hauberks and bishop's mantles used this method to create a standing collar. Other hauberks included a few individual leather thongs through the mail around the arms and leges to help the garment maintain its shape.
However, the type of armor which the Dungeons and Dragons authors referred to as "banded mail" is quite real. Because of the way the human torso flexes, an armor composed of horizontal bands of metal can provide excellent protection without significantly restricting the wearer's mobility. This style of armor was developed independently all over the world.
This style of armor was never referred to as "banded mail" before the nineteenth century. It was referred to as "anime" in the sixteenth century.
An extensive discussion of the use of this armor in Asia can be found at: http://www.geocities.com/Athens/Olympus/3505/page7.html