Jayne's Khaki coat makes several appearances, most notably in Jaynestown.
More after the break...
More screencaps from Jaynestown:
He also wears it in Trash:
And of course, The Train Job:
Jayne has several other coats in Firefly. One is his green jacket and another is his camo coat.
He also wears this khaki coat with one of his hats.
My Photobucket Album for Jayne.
Serenifly Costumes site for Jayne.