G-10 is now the preferred material. It used to be vulcanized fiber, and many still use it. The GF-10 is stronger, stiffer, won't shrink/swell, and comes in thing sizes now.
Here is how to get a really well matched composite handle.
First, roughen all mating surfaces to 100 grit. You need resin between the surfaces, and dead flat 400 grit surfaces don't glue up as well.
Next, use a slow cure structural resin. West System G-Flex and System Three T-88 are excellent.
The procedure:
Set a sheet of waxed paper on a 10X3" piece of flat wood or other flat surface that a clamp can fit on. Put down the liner material (normally about 5" by 3"). Spread the top with epoxy. Set the rear wood on the liner, coat the sides of the thin 3" strip of spacer and set it in place, and place on the front bolster wood. It is good if they are all a little longer than the liner by 1/4 to 1/2 inch. Lift the waxed paper and slip a block of wood up against the ends. Clamp one block down, and push the other up against the handle with just enough pressure to provide sufficient tension to make the bolster/spacer/handle seat snug against each other. Clamp the second block in place while holding this tension.
Lay a piece of waxed paper over the handle assembly, and put a single small spring clamp on the bolster and handle. I use the tiny el-cheapos from HF. All you need to do is hold them down on the liner securely while the resin cures overnight.
The next day, saw the assembled slab piece into two scales. Drill for rivets/bolts, and shape and polish the fronts while pinned together. Roughen the mating surfaces with 100 grit and assemble the handle on the tang.
This should assure perfectly matched handles sides.