The oldest of the double-mallet grips, the traditional grip, probably came about soon after the xylophone with the modern keyboard layout (instead of the older longitudinal trapezoid layout of e.g. Polish xylophone virtuoso Joseph Gusikov (1806 – 1837)) found its way into the orchestras around 1900. Very little, if any, documentation existed of the grip until German percussionist Peter Sadlo (1962 -) in 1994 completed his dissertation Die Kunst des Schlagens which describes and analyzes the traditional grip among others. The following year in August, American marimbist Nancy Zeltsman (1958 -) had the article Traditional Four-Mallet Grip published in the magazine Percussive Notes. In 2003, Peter Sadlo released his book Hauptsache Mallets which to some extent is a summary of certain parts of his dissertation, and that features a detailed description of the traditional grip together with also the Burton, the Musser and the Stevens grip. In the same year Zeltsman’s book Four-Mallet Marimba Playing came out that contains a comprehensive description of the traditional grip and its use.
The traditional grip is the only cross-grip that has the secondary, outer mallet, below the primary, inner mallet. There seems to be two versions of the grip where one, represented by Zeltsman, always has the thumb on top of the inner mallet, and another, which Sadlo represents, that lets the thumb grip the mallet shaft from the side at small intervals. The first version is the one used by Theodor Milkov in this YouTube video: http://www.youtube.com/watch?v=X4Xm9He1uaY. The second version is mentioned in the Gary Burton (1943 -) video The 4 Mallet (Burton) Grip at http://www.vicfirth.com/education/keyboard/burton.php.
Among famous musicians that used or are using the traditional grip are for example Adrian Rollini (1903 – 1956) and Keiko Abe (1937 -).
Below are two images of my right hand demonstrating the traditional grip at the interval of a fourth on an instrument with 48 mm center to center between the naturals and with mallets that are 435 mm long and mallet shafts of 8 mm in diameter.
doublemalletgrips 
Yesterday I discovered the following interesting video by Theodor Milkov about his thoughts on the Traditional grip: http://www.youtube.com/watch?v=W3ki7YpPLmk
Brendan Thompson has invented the Thompson Double Traditional Grip. Watch the following video for one of the most humorous grip demonstrations ever: http://www.youtube.com/watch?v=xkO6fnipAUU
Miroslav Dimov keeps the Traditional grip alive together with a charming choreographical playing style, here in a very nice interpretation of the Scarlatti sonata K98: http://www.youtube.com/watch?v=jP5woAYEGxg
The traditional cross grip is the only grip that for me provides needed flexibility and is inherently intuitive and natural, especially if the vibraphone (or in fact any mallet instrument) is viewed more like the piano which I feel is the correct way to approach it. I feel that the traditional cross grip is significantly superior and more logical than say the Burton grip which I personally find to be very unnatural and awkward, and so accordingly I’ve been using the traditional grip on vibes since 1976. Using the traditional grip allows the player to put both mallets in the right hand next to each other and to use both mallets in the right hand for melodic purposes along with the inner mallet in the left. Smoother and more logical phrasing is then possible. We don’t play piano melodies or improvised lines with the 5th finger on each hand, but rather more with the inner fingers of the right (and sometimes left) hand; the traditional grip most closely mirrors playing the vibraphone with mallets as an extension of one’s hand. I would also argue that it is a better extension/evolution of playing with two mallets when then learning to play with four (or five) mallets using the inner mallets to play melodic lines than being forced to use the outer mallet in the right hand. I don’t have any problem with the outer mallet not remaining stable and have plenty of power as well.