The phase behavior and its linear viscoelastic responses of a biocompatible blend based on ethylene-vinyl acetate copolymers and poly(e-caprolactone) (EVA/PCL) were studied in this work in terms of blending ratios and annealing. The effects of viscosity ratios and vinyl acetate contents of the EVA on the co-continuous morphology were addressed. The results show that EVA/PCL is a typical immiscible blend due to the high interfacial tension between the two polymers. Thus, the blend shows a wide percolation range with a narrow fully co-continuous region. Although the phase inversion point can be well predicted by the viscous Utracki model, the dynamic viscoelastic responses of the blend cannot be well described by the emulsion model. The elasticity ratio was proposed to play an important role together with the viscosity ratio on the phase inversions. During dynamic annealing, the phase size of both the sea–island and the co-continuous structures increases evidently, but the principle of time–temperature superposition is only valid for the co-continuous blend while fails with that with the sea–island phase structure. Beside, the phase size of the co-continuous structure is dependent strongly on the viscosity ratio between EVA and PCL. With reduced viscosity ratio, the phase size increases remarkably. However, vinyl acetate (VA) contents of the EVA have little influences on the interfacial properties and phase size of the co-continuous blends in the experimental content ranges (28–12 wt.%).