In recent years, utility-scale hybrid power plants (HPPs) have emerged as promising electricity generation resources by combining multiple generation technologies and storage capabilities. This paper presents a novel framework for optimizing the offering and operation of HPPs in the voluntary balancing market, specifically for providing regulating power as a balancing service. The proposed framework utilizes a two-level robust optimization approach, where the first level focuses on look-ahead offering and operation, and the second level handles real-time re-scheduling of generation. Uncertainties arising from wind power and regulating prices are considered as decision-independent uncertainties (DIU). Conversely, the decisions regarding regulating power offers influence the uncertainty associated with activated regulating volumes, leading to decision-dependent uncertainties (DDU). To tackle the model incorporating both DIU and DDU, this paper introduces a customized nested adaptive column and constraint generation (NAC&CG) algorithm that ensures global convergence. The case studies demonstrate the effectiveness of the proposed model in enabling HPPs to accurately track the activated regulating volumes, ensuring reliable provision of balancing service.