Driving behavior significantly impacts battery health. Existing research mainly improves battery health through powertrain and vehicle control. However, they rarely isolate and quantify the contribution of driving behaviors, which may lead to overestimating theoretical gains and underperformance in practice. To address this gap, this study introduces an integrated framework that links daily driving behavior to long-term battery health. The framework establishes a multiscale dynamic driving environment that integrates battery cell processes, powertrain systems, and vehicle-level driving behavior, enabling the estimation of real-time battery health influenced by driving behavior. Moreover, the problem formulation of the battery health-aware framework extends beyond traditional fixed driving cycles to dynamic driving scenarios that incorporate energy efficiency, battery health, and safety. Furthermore, second-level driving behaviors are linked to year-to-year battery health. Experiments across different travel demands and regions demonstrate that more stable driving behavior decreases energy consumption by 15.7% and reduces battery degradation by 10% over 10 years, with equivalent degradation occurring in 5 years under intensive travel. This work provides a cross-temporal quantitative framework that reveals the independent impact of driving behavior on battery degradation, supporting next-generation eco-driving and policy design.