The increasing interest in developing emulsion-based foods employing various combinations of plant-dairy proteins necessitates a thorough understanding of how to integrate these protein mixes into both existing and novel formulations. This study aimed to evaluate the stability and physical properties of emulsions enriched with a functional ingredient, Mentha essential oil (MEO), at the oil–water interface within systems containing different mixtures of whey protein with plant proteins such as soy and pea protein isolates. Emulsions with three different protein compositions were prepared using ultrasonication by incorporating Mentha essential oil. The emulsions were characterized for their physical properties, including droplet size distribution, zeta potential, emulsifying stability against creaming and coalescence, viscosity, and antioxidant properties. The oxidative stability of these emulsions was assessed by analyzing volatile lipid oxidation compounds throughout the storage period (28 days at 45°C). Their physicochemical properties were assessed through measurements of droplet size, viscosity, and creaming index. The results indicated that the emulsion containing pure whey protein produced smaller droplets (124.2 nm), exhibited a higher zeta potential (−50.8 mV), and formed a more viscous emulsion (1.89 mPas) compared to the emulsion containing soy and pea proteins (181.4 nm; −36.8 mV; 1.62 mPas). The protein composition had no significant effect on creaming stability. Moreover, emulsions prepared with soy and whey showed a higher scavenging activity for ABTS+ and DPPH radicals as compared to those prepared solely with whey protein. This study suggests that emulsions produced with whey protein exhibit excellent physical stability against flocculation, coalescence, and creaming, as well as a high stability against lipid oxidation. Further studies should be focused on the pretreatments of plant proteins to improve their techno-functional properties, for their effective administration into food delivery systems.