As a key and weak point of continuous fiber-reinforced composites (CFRCs), the interface between the fiber and the matrix is vulnerable to failure under external loads, with its performance directly affecting the overall properties of CFRCs. Hence, a micro–macro coupling method that considered the microscopic properties of the interface was utilized to analyze and predict the mechanical properties of CFRCs more accurately. The microscopic mechanical parameters of the fiber–matrix interface, which were obtained using molecular dynamics, were transferred to the representative volume element (RVE). The stiffness matrix of the CFRC, required for the macroscopic finite element model, was then calculated using a unified periodic homogenization method based on the RVE and assigned to the finite element model for a macroscopic simulation. Nylon/continuous carbon fiber specimens were fabricated through additive manufacturing, with the tensile and bending strengths of the specimens obtained through tensile and three-point bending tests. The tensile strength of the experimental specimen was 200.1 MPa, while the result of the simulation containing the interface was 205.5 MPa, indicating a difference of less than 5% between the two. In contrast, the result of the simulation without an interface was 317.7 MPa, representing a high error of 58.7% compared with the experimental results. Moreover, the bending strength, Young’s modulus, and flexural modulus results with and without an interface showed the same trend as that for the tensile strength. This illustrates the effectiveness of the proposed micro–macro coupling method for analyzing and predicting the mechanical properties of CFRCs.