Graphene oxide (GO) and multi-walled carbon nanotubes (MWCNT) have been previously used independently as active supports for layered double hydroxides (LDH), and found to enhance the intrinsic CO2 sorption capacity. However, the long-term stability of the materials subjected to temperature-swing adsorption (TSA) cycles still requires improvement. In this contribution, GO and MWCNT are hybridized to produce mixed substrates with improved surface area, and compatibility for the subsequent deposition of LDH platelets, compared to either phase alone. The incorporation of a robust and thoroughly hybridized carbon network considerably enhances the thermal stability of activated, promoted LDH over twenty cycles of gas adsorption-desorption (96% of retention of the initial sorption capacity at the 20th cycle), dramatically reducing the sintering previously observed when either GO or MWCNT were added separately. Detailed characterization of the morphology of the supported LDH, at several stages of the multicycle adsorption process, shows that the initial morphology of the adsorbents is more strongly retained when supported on the robust hybrid GO/MWCNT network; the CO2 adsorption performance correlates closely with the specific surface area of the adsorbents, with both maximized at small loadings of a 1:1 ratio GO:MWCNT substrate.