Herein, the effects of the contents of emulsified asphalt, waterborne epoxy resin emulsion, and curing agent on the permeability, bond shear strength, water stability, and aging resistance of epoxy-emulsified asphalt were studied. A formulation of epoxy-emulsified asphalt as a fog-sealing adhesive material was recommended, and a comparison between the fabricated adhesive material and a traditional Chinese fog-sealing adhesive material was conducted to verify the technical performance of the new material. In addition, the strength formation mechanism of the epoxy-emulsified asphalt was revealed via microcosmic analysis. Results show that the curing agent content mainly affects the permeability of epoxy-emulsified asphalt, and the emulsified asphalt content significantly affects the bond shear strength, water stability, and aging resistance. Moreover, the ratio of waterborne epoxy resin emulsion to the curing agent (epoxy ratio) has a certain effect on the bond shear strength. In the recommended formulation (a high-permeability and high-bonding fog-sealing adhesive material, which can be referred to simply as HPBFA), emulsified asphalt accounts for 80% of the total mass of the mixture, and the epoxy ratio is 2:1–3:1. It can improve air permeability, bond shear strength, water stability and aging resistance. The HPBFA-cured material exhibits a continuous three-dimensional network structure, hydrophobic surface, and large contact angle. Furthermore, the initial thermal weight loss temperature of the HPBFA-cured material is significantly higher than the environmental aging temperature. Additionally, the maximum temperature decomposition range is 0–160 °C, indicating improved strength, wear resistance, permeability, and aging resistance of the material.