The topic of modification of magnesium oxychloride cement (MOC) using specific functional additives is very much pronounced in the research of alternative building materials. This study deals with the co-doping of MOC by 1D and 2D carbon nanomaterials in order to improve its mechanical properties while using tannic acid (TA) as a surfactant. Furthermore, the effect of TA on MOC also improves its water resistance. As a filler, three size fractions of standard quartz sand are used. The proposed types of MOC-based composites show promising results considering their mechanical, macro- and microstructural, chemical, and hygric properties. The use of 1D and 2D nanoadditives and their mixture enables the improvement in the flexural strength and particularly the softening coefficient, which is the durability parameter characterizing the resistance of the prepared materials to water. After immersion in water for 24 h, the compressive strength of all tested specimens of modified composites was higher than that of the reference composite. Quantitatively, the developed co-doped composites show mechanical parameters comparable to or even better than those of commonly used Portland cement-based materials while maintaining high environmental efficiency. This indicates their potential use as an environmentally friendly alternative to Portland cement-based products.