Connected and autonomous vehicles (CAVs) are expected to significantly improve traffic efficiency and safety. However, the overall impacts of CAVs on mixed traffic have not been clearly studied because most previous research focused on one subset of the performance of mixed traffic. This study aims to provide complete information for the policymakers to make better decisions on future CAV implementation strategies with a comprehensive evaluation of the overall performance of mixed traffic. With this purpose, this study develops an integrated framework to evaluate the efficiency and safety of mixed traffic with CAVs under adverse weather conditions, which is composed of a traffic simulation, multi-vehicle crash model, single-vehicle crash model, and performance assessment. For the first time, a unified performance index is introduced to reflect the overall efficiency and safety performance of mixed traffic. The proposed framework is demonstrated with an evaluation of the performance of mixed traffic on a highway segment. Traffic efficiency and safety under different weather conditions are investigated. The impact of reaction time of human-driving vehicles (HDVs) and CAVs are also studied. Simulation results show that the overall traffic performance in terms of traffic efficiency, multi-vehicle safety, and single-vehicle safety increases with the increase in the market penetration rate (MPR). In addition, it is found that CAVs have a greater impact on improving overall traffic performance under rainy and snowy weather than in clear weather. Moreover, a shorter reaction time of HDVs and CAVs can lead to better overall traffic performance.