Effective coordination between electricity and carbon markets is critical for enabling energy-efficient decarbonization in integrated energy system. However, the inherent differences in trading products and timescales between two markets render independent electricity- carbon market mechanism invalid and target mismatch, particularly within multi-agent market environments. Hence, a multi-agent bi-level game model for park-level integrated energy system (PIES) is proposed in this paper, incorporating a novel electricity-carbon market collaborative decision-making mechanism. An equal-interval time discretization method is developed to reconcile the heterogeneity of discrete electricity market and continuous carbon market, enabling consistent timescale coordination. An improved alternating direction method of multipliers (ADMM) algorithm based on Peaceman-Rachford is adopted to achieve benefit allocation and rapid privacy-solving. Simulation results demonstrate the effectiveness of proposed multi-agent bi-level game model in balancing carbon reduction and economic efficiency, and enhancing the operation efficiency of multi-agent collaboration.