We explore the three-dimensional interaction of higher acoustic modes with bias-flow perforated liners in cylindrical and annular ducts. Pressure fluctuations in the vicinity of the liners excite the production and shedding of vorticity from the rims of apertures in the liners. An effective liner compliance is used which accounts for this transfer of acoustical into vortical energy. The investigation is facilitated by a Green's function solution of the Helmholtz equation in a lined section of duct, allowing calculation of the amplitudes of exiting wave modes due to incoming acoustic disturbances. A system containing an arbitrary number of concentric liners and the hollow cavities formed between them can be modelled. The results for an incident plane wave are compared with those from our previously developed one-dimensional model, with excellent agreement. We demonstrate that results for all modes that travel parallel to the liner, including higher circumferential modes in narrow annular gaps, exhibit self-similar behaviour, and that liner design rules developed for planar duct modes can be adapted accordingly. The acoustic absorption can be strongly enhanced by downstream duct reflection for wavelengths larger than twice the liner length, but is less affected at higher frequencies that allow persistent pressure minima along the liner. Across larger frequency ranges, the liner systems are shown to permit two types of resonance associated with the duct and the cavities, respectively, and a third of Helmholtz type, associated with the system as a whole. The effect of these resonances on incident modes is demonstrated, and, in particular, we explore their enhancement of acoustic absorption.