There are many variations seen in American swivel breeches, as well as two areas covered by your question. I don't know which one you are asking, so will give short answers to each possibility. My list of carefully examined and documented 18th and 19th Century Kentucky double rifles for my ongoing study is past 60 now, and many different solutions are seen in originals. I think you are asking
(1) how the barrels are fastened to each other.
The wording could also refer to
(2) how the barrels are fastened to the swivel plate that rotates with the barrels.
Answer #1)
A) Louie describes an elegant method seen on good rifles which are full stocked. Those guns are not "full paneled", but have a single piece fore stock with two barrel inlets in it (by far the most common method used in full stocked swivels).
B) Some have only two "side by side" lugs (slightly offset to each side) with one pin.
C) Others have the opposing barrel lugs staggered lengthwise and each with its own pin. Most barrels use 3 or 4 pins in the length of the barrel (6 or 8 in using one pin for one lug).
D) A few later ones use keys with similar arrangements.
In these full wood stocked doubles, the rod thimbles are usually screwed on from the other side through an escutcheon, but occasionally are made with a tab and pinned from top to bottom in the barrel channels, much as a single barreled rifle is pinned across under the barrel channel.
E) In rifles with metal fore ends or ribs or even bare, most are soft soldered along the touching flats.
F) At least one has opposed dovetails with "bow tie" wedges ( it was loose).
As to fastening to the swivel plate, square lugs integral with the breech plugs are often set in square holes in the swivel plate and screwed or pinned parallel with the face of the plate. Some are done with dove tailed breech plug "tangs" screwed vertically or pinned transversely, or with hook breech plugs as seen in patent breeches. Jaegers are frequently fastened with screws from behind into the square breech plug (parallel to and concentric with the bore) and of course countersunk as the head is on the swivel bearing face. Some originals have a combination of hook and square pinned plug, or dovetail and square plug. Lots of variation is seen, and many are loose at the barrel/ swivel plate interface.
I will be interested in hearing more about your build!
Bill Paton 907-230-3600 wapaton.sr@gmail.com