Assessing and analyzing the complementary characteristics of renewable energy (RE) is crucial for designing, operating, and optimizing multi-energy complementary systems (MECSs). However, unified and precise quantitative descriptions of the complementary and stability characteristics among various energy outputs in MECSs have lacked attention and research. Here, this study innovatively proposed a mathematical model for the multi-energy complementarity index (MECI), which considers the complementarity rates of multiple energy outputs during zero and non-zero output periods, and a mathematical model for the multi-energy volatility index (MEVI), which accounts for fluctuation thresholds and the overall volatility of output processes. An evaluation system for multi-energy complementarity characteristics qualitative analysis has been established. The natural output processes of RE at three MECSs in China were applied in the case calculations and verification. Results show that the hydropower rated discharge (Qrating) has a significant negative correlation with MECI, with the MECI decreasing by an average of 0.0046 for every 5 m³/s increase in Qrating. The relationship between the Qrating and MEVI shows an overall negative correlation with local fluctuations. Notably, The MECI of the BeiPan River MECSs exhibits significant seasonal characteristics, with the MEVI in summer (0.378) and autumn (0.395) higher than those in spring (0.132) and winter (0.160), closely related to the natural seasonal variations of the three energy sources: water, wind, and solar. We believe that the study can assist in evaluating and making decisions on the multi-energy complementarity characteristics of RE bases in the future, making a significant contribution to achieving dual carbon goals.