•Surrogate model is used to assist performance-based earthquake engineering.•Vector intensity measure is coupled with surrogate model to improve the PBEE.•Vine copula is used to capture the complex dependence within PBEE.•An updated PBEE framework is proposed by interconnecting several techniques.•The effect of dependence modeling on higher-order moments of performance is clarified. Performance-based earthquake engineering (PBEE) is an advanced philosophy for the design, assessment, and decision-making of structures under seismic hazards. Improving the accuracy and efficiency of PBEE is of great importance. In traditional cloud analysis, a linear regression is performed in the logarithmic space of seismic intensity measure (IM) and demand. The obtained relationship is used to predict the seismic demand. Then, some advanced models for seismic demand prediction were developed to improve the accuracy. There exists dependence within PBEE, whereas multivariate normality of logarithmic values is widely assumed for modeling the dependence in previous studies. This paper proposes a hybrid and novel framework to improve the seismic performance assessment. The proposed framework can improve confidence while capturing more realistic dependence. The vector IM and surrogate models are coupled to predict the seismic demand. The vine copula can characterize complex nonlinear dependence structures, and it is adopted to model the dependence of demands and IMs. Then, seismic performance can be assessed. The proposed framework is illustrated on bridges under seismic hazards. For the investigated cases, the proposed framework can improve confidence significantly and better capture complex dependence. Additionally, the effect of dependence modeling on higher-order moments of seismic performance is investigated. Within the investigated cases, the large difference of higher-order moments of seismic performance is observed by using conventional assumption and vine copula. The generality and flexibility of vine copula-based approach highlight the necessity of implementing the proposed framework.