The process in which the anatomical structures derived from the haltere disc are generated and organized. This includes the transformation of a haltere imaginal disc from a monolayered epithelium in the larvae of holometabolous insects into the recognizable adult capitellum, pedicel, haltere sclerite, metathoracic spiracle and metanotum. [ GOC:bf https://www.worldcat.org/search?q=bn%3A0879694238 ]