In incoherent digital holography (IDH) and in any imaging technique, the lateral and axial resolutions are intertwined and consequently changing one characteristic affects the other. In this study, we present two new hybridization techniques HM-1, and HM-2 for IDH, one for real-time and another for post-recording of holograms respectively, to engineer the axial resolution independent of lateral resolution. Two optical functions namely a lens and an axicon, with a low focal depth and a high focal depth respectively are considered. In both hybridization techniques, the axial resolution can be tuned between the limits of the axial resolutions of lens and axicon, while maintaining a constant lateral resolution. In HM-1, the axial resolution was engineered using a special phase mask designed using a modified version of Gerchberg-Saxton algorithm that can generate a spherical beam and Bessel beam for every object point and create self-interference between them. By controlling the strengths of the two beams, the axial resolution can be tuned without changing the lateral resolution. This method requires an active optical device such as a spatial light modulator. HM-2 involves two recordings of the same scene, one with a lens and another with an axicon which are then combined after recording. By controlling the weights of the two recordings, the axial resolution can be tuned between the limits of lens and the axicon independent of lateral resolution. In this case, passive diffractive or refractive optical elements are sufficient. Both hybridization techniques are implemented in indirect imaging mode consisting of three steps: recording point spread hologram, object hologram and reconstruction by Lucy-Richardson-Rosen algorithm.