Magnesium phosphate cement (MPC) has both traditional cement properties and ceramic properties with fast setting and hardening characteristics. To rapidly reopen traffic and extend its service life, MPC has been widely used in the rapid repair of highway and airport cement concrete pavement. This study utilizes basalt fiber-reinforced polymer-modified magnesium phosphate cement (BFPMPC) developed in previous research to rapid repair the typical potholes on cement concrete pavement, aims to reveal the interface properties between BFPMPC mortar and cement concrete and further investigate the underlying mechanisms for such properties. Firstly, the optimal mixture ratio was determined by orthogonal test design. Then, the shear strength of the repair interface was measured by composite BFPMPC mortar and cement concrete specimens. The mechanical characteristics of the repair interface and the microscopic mechanism were characterized by nano-indentation technology and SEM/EDS. Finally, the interface constitutive model was established by DIGIMAT and finite element model was developed to simulate the interface failure. Results showed that the no new hydration products were produced by the addition of polymer in BFPMPC. BFPMPC matrix became denser with the increase of age, resulting in the better bonding between fiber and paste. The interface vertical shear strength at 6 h and 3 d were 3.1 MPa and 3.9 MPa, respectively. SEM/EDS results showed that polymer has a certain self-healing ability to decrease the crack width with increase of curing age, and a variety of inclusions in the repair interface were observed. The elastic modulus of each inclusion phase can be effectively analyzed by nanoindentation. The simulation results showed that the pressure on upper surface of BFPMPC mortar transfers to the bottom through the repair interface. As the tensile stress on the bottom over the maximum interface tensile stress, the cracks were extend from the bottom to upper, then the structure was failed. Interface vertical shear strength of numerical simulation was, respectively, 3.149 MPa and 3.957 MPa. It is close to the plain shear strength experimental value, validating the proposed interface constitutive relationship.