Poly(ethylene-co-vinyl acetate) (PEVAc) is a copolymer that consists of non-polar polyethylene (PE) and a polar polyvinyl acetate (PVAc) monomer. PEVAc has high elasticity and is resilient, making it suitable for a variety of applications. However, the tensile strength of this copolymer needs to be improved for specific applications that require enough strength to tolerate high external tension or stress. This study proposed the use of dual-functionalized dolomite nanoparticles (DF-DNPs) composed of polar and non-polar nano-dolomite (P-DNPs and NP-DNPs) as nanofillers to reinforce the PEVAc. PEVAc/DF-DNP film appears to have a more homogeneous mixture, which is better for forming an optimal nanocomposite material. It also exhibits the highest tensile strength (10.48 MPa), elongation at break (1175.73%), and tensile toughness (62.12 MPa), which are higher by increments of 46.8%, 9.4%, and 20.3%, respectively, as compared to the neat PEVAc. The result proved that using DF-DNPs as a nanofiller can improve the strength of PEVAc while maintaining its flexibility to avoid brittleness of the nanocomposite film. Furthermore, its thermal characteristics were also successfully enhanced. A biostability assessment showed that the use of DF-DNPs as nanofiller caused the PEVAc copolymer to achieve the best water resistance, as it only exhibited a 2.63% weight increase, the lowest reduction in tensile properties among the studied fillers, and the best retention in surface degradation upon 3-month exposure to the in vitro environment. These findings indicate that the DF-DNPs help in developing a homogeneous nanocomposite by interacting with PE and PVAc.