Orientation and alignment parameters have been computed from first principles for the photodissociation of the HF and DF diatomic molecules. The calculations are entirely ab initio and the break-up dynamics of the molecule is treated rigorously taking account of the electronically nonadiabatic dynamics on three coupled adiabatic electronic potential energy curves. The potential energy curves and spin-orbit interactions, which have been previously reported [J. Chem. Phys. 113, 1870 (2000)], are computed using ab initio molecular electronic structure computer codes. These are then used to compute photofragmentation T matrix elements using a time-dependent quantum mechanical wave packet treatment and from these a complete set of anisotropy parameters with rank up to K=3 is computed. The predicted vector correlations and alignment parameters are presented as a function of energy for HF and DF initially in both their ground and first excited vibrational states. The parameters predicted for the molecules which are initially in their excited vibrational states display a pronounced sharp energy dependence arising from the nodal structure of the initial vibrational wavefunction. The theoretical results are analyzed using a simple model of the dynamics and it is demonstrated how the magnitude and relative phases of the photofragmentation T matrix elements can be deduced from the experimentally measured alignment parameters. No experimental measurements have yet been made of alignment parameters for hydrogen halide diatomics and the present results provide the first predictions of these quantities which may be compared with future experimental observations.