Based on elastic dumbbell model of polymer melt and tensor description of fiber orientation, a mathematic multi-scale model with a general equation for the non-equilibrium reversible-irreversible coupling (GENERIC) of polymeric melt with fiber suspensions is presented by the coupling of reversible and irreversible thermodynamics. And the model provides a general framework with homogeneous GENERIC structure for the multi-scale governing equations. Through analyzing the components of GENERIC structure, stress contributions from information on different scales can be achieved.