Various sources of uncertain parameters at multiple levels, from design steps to manufacturing processes, are often involved in composite structures. Probabilistic modeling and analysis of the composite structure and its manufacturing processes can provide underlying information to assess uncertainties and improve the quality of the developed composite structures. This paper presents a stochastic multilevel modeling framework considering material, structural, modeling parameters as well as the manufacturing process based on a surrogate model. An enhanced laminate theory is employed to determine the elastic constants of the composite materials considering imperfect bonding among filaments in the manufacturing process. To improve the computational efficiency in simulation-based reliability approach, the evaluation of the structure properties is approximated by employing surrogate models based upon the physics model. To apply the present framework, a case study with a composite laminate beam under three-point bending, which is made through fused deposition modeling, is conducted, and the case study results demonstrate the efficacy of the presented modeling scheme and analysis methodology.