In recent years, the development of ternary cements has become a priority research line for obtaining cements with a lower carbon footprint, with the goal to contribute to achieve climate neutrality by 2050. This study compared ordinary Portland cement (OPC) durability to the performance of ternary cements bearing OPC plus 7% of a 2:1 binary blend of either calcareous (Hc) or siliceous (Hs) concrete waste fines and shatterproof glass. Durability was measured further to the existing legislation for testing concrete water absorption, effective porosity, pressurized water absorption and resistance to chlorides and CO2. The experimental findings showed that the 7% blended mortars performed better than the reference cement in terms of total and effective porosity, but they absorbed more pressurized water. They also exhibited lower CO2 resistance, particularly in the calcareous blend, likely due to its higher porosity. Including the binary blend of CDW enhanced chloride resistance with diffusion coefficients of 2.9 × 10−11 m2 s−1 (calcareous fines-glass, 7%Hc-G) and 1.5 × 10−11 m2 s−1 (siliceous fines-glass, 7%Hs-G) compared to the reference cement’s 4.3 × 10−11 m2 s−1. The siliceous fines-glass blend out-performed the calcareous blend in all the durability tests. As the mortars with and without CDW (construction and demolition waste) performed to similar standards overall, the former were deemed viable for the manufacture of future eco-efficient cements.