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Polaritonic materials that support epsilon-near-zero (ENZ) modes offer the opportunity to design light-matter interactions at the nanoscale through extreme subwavelength light confinement, producing phenomena like resonant perfect absorption. However, the utility of ENZ modes in nanophotonic applications has been limited by a flat spectral dispersion, which leads to small group velocities and extremely short propagation lengths. Here, we overcome this constraint by hybridizing ENZ and surface plasmon polariton (SPP) modes in doped cadmium oxide epitaxial bilayers. This results in strongly coupled hybrid modes that are characterized by an anticrossing in the polariton dispersion and a large spectral splitting on the order of 1/3 of the mode frequency. These hybrid modes simultaneously achieve modal propagation and ENZ mode-like interior field confinement, adding propagation character to ENZ mode properties. We subsequently tune the resonant frequencies, dispersion, and coupling of these polaritonic-hybrid-epsilon-near-zero (PH-ENZ) modes by tailoring the modal oscillator strength and the ENZ-SPP spectral overlap. PH-ENZ modes ultimately leverage the most desirable characteristics of both ENZ and SPP modes, allowing us to overcome the canonical plasmonic trade-off between confinement and propagation length.