The paper analyzes the correlation features between stress strength, multiple failure mechanisms, and multiple components. It investigates the effects of different correlation features on reliability and proposes a method for structural reliability analysis that considers the joint effects of multiple correlation features. To portray the stress–strength correlation structure, the Copula function is utilized and the influence of the correlation degree parameter on reliability is clarified. The text describes the introduction of time-varying characteristics of structural strength and correlation parameters. A time-varying Copula is then constructed to calculate the structural reliability under the stress–strength correlation characteristics. Additionally, a time-varying hybrid Copula is constructed to characterize the intricate and correlation features of multiple failure mechanisms and components. The article proposes the variational adaptive sparrow search algorithm (VASSA) to obtain optimal parameters for the time-varying hybrid Copula. The effectiveness and accuracy of the proposed method are verified through actual cases. The results indicate that multiple correlation features significantly influence structural reliability. Incorporating multiple correlation features into the solution of structural reliability yields safer results that align with engineering practice.