This study proposes a new dense membrane for selectively separating CO₂ and O₂ at high temperatures and simultaneously producing syngas. The membrane consists of a cermet-type material infiltrated with a ternary carbonate phase. Initially, the co-doped ceria of composition Ce_0.9Zr_0.05Y_0.05O_2−δ (CZY) was synthesized by using the conventional solid-state reaction method. Then, the ceramic was mixed with commercial silver powders using a ball milling process and subsequently uniaxially pressed and sintered to form the disk-shaped cermet. The dense membrane was finally formed via the infiltration of molten salts into the porous cermet supports. At high temperatures (700–850 °C), the membranes exhibit CO₂/N₂ and O₂/N₂ permselectivity and a high permeation flux under different CO₂ concentrations in the feed and sweeping gas flow rates. The observed permeation properties make its use viable for CO₂ valorization via the oxy-CO₂ reforming of methane, wherein both CO₂ and O₂ permeated gases were effectively utilized to produce hydrogen-rich syngas (H₂ + CO) through a catalytic membrane reactor arrangement at different temperatures ranging from 700 to 850 °C. The effect of the ceramic filler in the cermet is discussed, and continuous permeation testing, up to 115 h, demonstrated the membrane’s superior chemical and thermal stability by confirming the absence of any chemical interaction between the material and the carbonates as well as the absence of significant sintering concerns with the pure silver.