A theoretical formalism is developed for the quantum-state-specific photoelectron angular distributions (PADs) from the direct photoionization of a diatomic molecule in which both the ionizing state and the state of the ion follow Hund’s case (b) coupling. The formalism is based on the molecular-orbital decomposition of the ionization continuum and therefore fully incorporates the molecular nature of the photoelectron-ion scattering within the independent electron approximation. The resulting expression for the quantum-state-specific PADs is dependent on two distinct types of dynamical quantities, one that pertains only to the ionization continuum and the other that depends both on the ionizing state and the ionization continuum. Specifically, the electronic dipole-moment matrix element r(l lambda) exp(i eta(l lambda)) for the ejection of a photoelectron with orbital angular momentum quantum number I making a projection lambda on the internuclear axis is expressed as Sigma(alpha lambda) <(U)over bar(l alpha lambda)(lambda)> exp(i pi tau(alpha lambda)(-lambda))M(alpha lambda)(alpha), where <(U)over bar(lambda)> is the electronic transformation matrix, tau(alpha lambda)(lambda) is the scattering phase shift associated with the alpha(lambda)th continuum molecular orbital, and M(alpha lambda)(lambda) is the real electronic dipole-moment matrix element that connects the ionizing orbital to the alpha(lambda)th continuum molecular orbital. Because <(U)over bar(lambda)> and tau(alpha lambda)(lambda) depend only on the dynamics in the ionization continuum, this formalism allows maximal exploitation of the commonality between photoionization processes from different ionizing states. It also makes possible the direct experimental investigation of scattering matrices for the photoelectron-ion scattering and thus the dynamics in the ionization continuum by studying the quantum-state-specific PADs, as illustrated in the companion article on the photoionization of NO.