High spatial resolution, narrow band, infrared line images and CO (1 - 0) mm interferometer data are presented for NGC 7027. These data trace emission from the central H II region (Bralpha), the intermediate photodissociation region [H-2 1 - 0 S(1) and 3.3 mum dust feature], and the molecular circumstellar envelope [CO (1 - 0)]. The H II region lies in a cavity in the CO envelope, and consists of a smooth elliptical shell. A striking change of morphology is seen in the H-2 emission and the dust feature. The H-2 1 - 0 S(l) emission is composed of two components: (1) an incomplete elliptical ring of knots which bounds the ionized gas; (2) a remarkable thin shell which loops around the H II region with fourfold symmetry. The dust emission is similar to that from the ionized gas, but is displaced further from the center, and extends at low surface brightness into four ''ears'' which fill in the bays delineated by the outermost loops of H-2 emission. No 3.3 mum emission is detectable beyond the outer H-2 shell. The outer loops of H-2 emission and the 3.3 mum emission occupy the region between the edge of the H II region and the inner edge of the molecular gas. It is natural to ascribe the morphology of NGC 7027 to a photodissociation region which separates the ionized and molecular gas. If this is correct then the exterior H-2 loops are due to molecular ps heated by the far-UV emission escaping from the H II region, and delineate a photodissociation front. The H-2 and CO kinematics rule out shock excitation of the H-2 emission and favor UV excitation.