A series of (1-x)GeS2.5-xSb chalcogenide glasses were prepared using the conventional melt-quenching method. Their microstructure and thermal response were systematically studied. We observe a compositional threshold of x=0.25 which corresponds to chemical stoichiometric composition in the calorimetric experiments. It is in good accordance with the Raman scattering results and laser-induced phase transformation behavior. They also indicate that phase separation of Sb-rich phase exists in the S-poor samples. Moreover, we got a structural modeling of this phase separation: (1) at x=0.25, which is chemical stoichiometric composition, the structural motifs are only SbS3 pyramid and GeS4 tetrahedra, and the three-coordinated SbS3 pyramid is isolated by GeS4 tetrahedra; (2) at x<0.25, the S-S bonds exist in the glass network due to the excess of S; and (3) at x>0.25, the excess of Sb break the Ge-S and Sb-S bonds to form Sb(Ge)-Sb Bonds, and the Sb atoms segregate from the backbone to nucleate a separate Sb-rich phase. This work provides a new way to investigate the phase separation of glass networks and helps us to better understand their related physical properties.