Photonic integrated microcombs have enabled advanced applications in optical communication, microwave synthesis, and optical metrology, which in nature unveil an optical dissipative soliton pattern under cavity-enhanced nonlinear processes. The most decisive factor of microcombs lies in the photonic material platforms, where materials with high nonlinearity and in capacity of high-quality chip integration are highly demanded. In this work, we present a home-developed chalcogenide glasses-Ge25Sb10S65 (GeSbS) for the nonlinear photonic integration and for the dissipative soliton microcomb generation. Compared with the current integrated nonlinear platforms, the GeSbS features wider transparency from the visible to 11-μm region, stronger nonlinearity, and lower thermo-refractive coefficient, and is CMOS compatible in fabrication. In this platform, we achieve chip-integrated optical microresonators with a quality (Q) factor above 2×10^6, and carry out lithographically controlled dispersion engineering. In particular, we demonstrate that both a bright soliton-based microcomb and a dark-pulsed comb are generated in a single microresonator, in its separated fundamental polarized mode families under different dispersion regimes. The overall pumping power is on the ten-milliwatt level, determined by both the high Q-factor and the high material nonlinearity of the microresonator. Our results may contribute to the field of nonlinear photonics with an alternative material platform for highly compact and high-intensity nonlinear interactions, while on the application aspect, contribute to the development of soliton microcombs at low operation power, which is potentially required for monolithically integrated optical frequency combs.