A model for photoassociation of ultracold atoms and molecules is presented and applied to the case of 39K and 23Na39K bosonic particles. The model relies on the assumption that photoassociation is dominated by long-range atom-molecule interactions well outside the chemical bond region. The frequency of the photoassociation laser is chosen close to a bound-bound rovibronic transition from the X1Σ+ ground state toward the metastable b3Π lowest excited state of 23Na39K, allowing us to neglect any other excitation, which could hinder the photoassociation detection. The energy level structure of the long-range 39K···23Na39K excited super-dimer is computed in the space-fixed frame by solving coupled-channel equations, involving the coupling between the 23Na39K internal rotation and the mechanical rotation of the super-dimer complex. A quite rich structure is obtained, and the corresponding photoassociation rates are presented. Other possible photoassociation transitions are discussed in the context of the proposed model.