Wendell Wolka of Sun City Center, FL writes:

The explanation I have seen of the printing does not explain the process very well. Dave Bowers on page 334 of his 2006 Obsolete Paper Money volume points to the explanation in the 1864 Heath's InfallibleCounterfeit Detector, which provides an example of the process as Plate 8. Heath's explanation is as follows (he's referring to the color printing of, say, FIVE or some other denomination on both sides of a banknote):

As someone who prints intaglio, this explanation is a little hard to envision in practice. And it does not seem to explain the perfect registration, face to back, but if the piece of thick paper is exactly the size of thetint plate, maybe that's part of the answer. Perhaps others know of better explanations.

In any case I believe the purpose of the two sided printing is the perfect registration "see-through" effect, which would be difficult to duplicate. Interestingly, this "see-through" concept is verymuch used on current international bank notes, nicknamed "c-thru" by the modern era bank note designers.