Thin hexagonal boron nitride layers have been shown to support highly confined hyperbolic phonon-polaritons, which are of interest for light guiding applications. Localized plasmon resonances in nanopatterned metal films can exhibit subwavelength-scale confinement as well as a high local field strength that is of importance to imaging and sensor applications. In this work, the interaction between hyperbolic phonon-polaritons in a hexagonal boron nitride thin film and plasmon-polaritons in a nanopatterned gold thin film is investigated by means of finite-difference time-domain simulations of a series of coupled and uncoupled layered devices. Both far-field and near-field properties are calculated and analyzed, enabling the features due to plasmon-polaritons and phonon-polaritons, individually, to be distinguished and the coupling between these excitations to be explored and characterized.