In the present study, reverse nonequilibrium molecular dynamics is employed to study thermal resistance across interfaces comprising dimensionally mismatched junctions of single layer graphene floors with (6,6) single-walled carbon nanotube (SWCNT) pillars in 3D carbon nanomaterials. Results obtained from unit cell analysis indicate the presence of notable interfacial thermal resistance in the out-of-plane direction (along the longitudinal axis of the SWCNTs) but negligible resistance in the in-plane direction along the graphene floor. The interfacial thermal resistance in the out-of-plane direction is understood to be due to the change in dimensionality as well as phonon spectra mismatch as the phonons propagate from SWCNTs to the graphene sheet and then back again to the SWCNTs. The thermal conductivity of the unit cells was observed to increase nearly linearly with an increase in cell size, that is, pillar height as well as interpillar distance, and approaches a plateau as the pillar height and the interpillar distance approach the critical lengths for ballistic thermal transport in SWCNT and single layer graphene. The results indicate that the thermal transport characteristics of these SWCNT-graphene hybrid structures can be tuned by controlling the SWCNT-graphene junction characteristics as well as the unit cell dimensions.