We theoretically investigate mid-infrared electromagnetic wave propagation in multilayered graphene-hexagonal boron nitride (hBN) metamaterials. Hexagonal boron nitride is a natural hyperbolic material that supports highly dispersive phonon polariton modes in two Reststrahlen bands with different types of hyperbolicity. Due to the hybridization of surface plasmon polaritons of graphene and hyperbolic phonon polaritons of hBN, each isolated unit cell of the graphene-hBN metamaterial supports hybrid plasmon-phonon polaritons (HPPs). Through the investigation of band structure of the metamaterial we find that, due to the coupling between the HPPs supported by each unit cell, the graphene-hBN metamaterial can support HPP bands. The dispersion of these bands can be noticeably modified for different thicknesses of hBN layers, leading to the appearance of bands with considerably flat dispersions. Moreover, analysis of light transmission through the metamaterial reveals that this system is capable of supporting high-k propagating HPPs. This characteristic makes graphene-hBN metamaterials very promising candidates for the modification of the spontaneous emission of a quantum emitter, hyperlensing, negative refraction, and waveguiding. © 2017 Optical Society of America.