To address the challenge that uncertainties in renewable energy sources and loads hinder the achievement of zero-carbon targets in integrated energy systems (IES), this paper proposes a zero-carbon capacity planning and multi-time-scale optimization method for IES considering uncertainties. Taking an IES in Xinjiang with electric, heating, and cooling load demands as the study case, a multivariate joint distribution combined with the Monte Carlo method is first employed to model the uncertainties and correlations of renewable energy sources and loads. Then, a whole life-cycle zero-carbon capacity planning method for IES is proposed, in which carbon dioxide is absorbed by alkaline solution generated during the electrolysis process of hydrogen energy storage. Finally, a zero-carbon emission dispatch framework over the IES planning horizon is constructed to coordinate zero-carbon optimization across long-term planning and short-term dispatch cycles. Based on this framework, a stochastic-rolling two-stage optimization dispatch model is designed to cope with uncertainties in renewable energy and load, aiming to minimize the overall operation cost of the IES. Simulation results verify the effectiveness of the proposed method in promoting renewable energy consumption, reducing primary energy usage, and achieving zero-carbon emissions with economic operation.