In the present paper, a two-scale FE technique based on periodic homogenization theory is investigated to predict the macroscopic non-linear behavior of polymer matrix composite structures. The computational technique accounts for the fiber/matrix interfacial damage, the matrix ductile damage and the effect of 3D periodic microstructure. The developed approach integrates the geometric description and the non-linear time-dependent local behavior of the different constituents (fibers, matrix and interface). For numerical calculations, advanced User Defined Material and User Element subroutines are developed at the two scales, simultaneously activated to solve macroscopic and microscopic problems through an incremental scheme in the finite element commercial code Abaqus/Implicit. The computational efficiency of the developed multi-scale approach is demonstrated by predicting the overall response of 3D composite structures under complex loading paths. The composite structures consist of thermoplastic polymer matrix with elasto-viscoplastic behavior and ductile damage, reinforced by elastic aligned short fibers that are coated by a cohesive zone, which obeys the general unified potential. The numerical results obtained by FE2 simulation with and without accounting for interface effect are analyzed and compared for two examples: Meuwissen-like and 3D corner shape structures. The main benefits of the developed approach lie in accessing the microscopic strain fields, the distributions of the internal variables and the damage evolution in both polymer matrix and interface, as well as identifying their repercussions on the macroscopic response.