Tailored jacket sleeves are fullly interfaced and lined. The interfacing historically is horsehair, but there are modern wool (faux and real) interfacings that are purposely for tailoring. One must be careful with fusible interfacing, and I don’t particularly recommend it for historical fashions. Sew-in is the way to go! But a frockcoat shouldn’t have sleeves that “drape.” They need to be shaped and the inner layers help with that.

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That is indeed my chemise sleeve visible under the sheer white windowpane fabric of the Regency dress. The dress itself is fully un-lined – no underlining fabric at all even on the bodice.

(And don’t worry, this sleeve article is much newer than the bodice and skirt flatlining posts. You didn’t bypass it – I hadn’t published it yet! 😉 )

The fitted stay is like a short sleeve that basically goes around your upper arm and is the cap length you want. Then you gather up the puff to fit the stay sleeve at the top and bottom, baste, and set into the armhole. You can add netting or other stuffing between the puff and stay to help hold the puff out in its shape. It’s so you don’t have your arm simple sitting inside the huge puff; it’s controlled by the stay. Hope this helps.