Proper co-optimization of photovoltaic driven air conditioning (PVAC) systems with load flexibility and batteries is pivotal for achieving zero energy buildings (ZEBs). However, practical implementation faces challenges from separate optimization with conflicting objectives, neglect of spatial-temporal occupancy features, and limited consideration of energy, economic, and environmental performance. This study proposes a hierarchical multi-objective co-optimization framework for capacity design and control strategy of the PVAC coupling systems, with the two optimization layers sharing the same multi-objective function. The optimization method balances energy, economic, environmental performance by key metrics including thermal comfort satisfaction ratio (TCSR), grid cumulative action power (GP_total), net present value (NPV) and emission reduction (ER). The optimal capacity optimization of PV and batteries for PVAC systems was solved by the NSGA-II and TOPSIS algorithms. Based on the case study of a multi-functional academic building, the optimization results of the off-grid system and the grid-connected system were calculated under different configuration of PV and battery capacity, and the relationship between the indicators was discussed. The optimization method of off-grid PVAC systems achieves 24 % reduction in PV capacity while maintaining 85.85 % TCSR, 123,800 CNY of NPV, and 167.26 tons of ER. Grid-connected systems with 165.88 kW PV capacity and 71.26 kWh battery capacity can achieve 100 % of TCSR, 1861.8 kW of GP_total, 148,300 CNY of NPV, and 174.70 tons of ER. The study provides an innovative and practical method for capacity design and energy control of PVAC coupling systems to achieve zero energy buildings.