A quantum mechanical treatment of the photofragment angular momentum polarization following photodissociation of diatomic molecules is presented. This treatment extends that of Siebbeles [J. Chem. Phys. 100, 3610 (1994)] by considering photodissociation of a molecule whose angular momentum is polarized in the laboratory frame, and also treats properly the angular momentum coupling between the two photofragments. The formalism treats coherent excitation of dissociative surfaces and the consequences of nonadiabatic coupling between surfaces. The possibility of exploiting the parent molecule polarization in order to control the photofragment polarization when both parallel- and perpendicular-type dissociations are active is discussed. An example is given in which significant control over the molecular frame polarization of the fragments is achieved following photolysis of a parent molecule prepared by an electric dipole transition, which may be of use in the study of photoinitiated bimolecular reactions.