The envelope comprises layers of plain un-coated kraft paper and of bubble-wrap polyethylene. A stack of the layers is joined at the marginal edges of the envelope by squeezing the stack between a pair of points-dies, which are formed with points that puncture the kraft paper but do not puncture the polyethylene. The points push crowns of un-punctured polyethylene through the punctured boles in the paper. Then, the marginal edges are squeezed flat between flat-dies, the flat-dies being heated enough to cause fuse-bonding. The margins of the finished envelope are held together not only by fuse-bonding, but by the presence of the crowns, which, penetrating right through the holes in the paper, serve as mechanical rivets.