The accurate measurement of total electron content (TEC) is vital for ionospheric research and satellite navigation services. Nowadays, the advancement of multiple Global Navigation Satellite System (multi-GNSS) has resulted in over 100 seamlessly spaced satellites and thousands of publicly available GNSS stations globally, which enables precise estimation of global ionospheric TEC and differential code biases (DCBs). However, challenges persist in eliminating system differences and leveraging the advantages of multi-GNSS big data due to frequency variances and hardware delays. Here, we propose a novel estimation method that incorporates satellites, constellations, stations, and time constraints for joint global ionospheric TEC and DCB estimation to improve the consistency and reliability of the usage of global observation data from multi-GNSS systems. The results show that the global vertical TEC map derived from approximately 5000 global multi-GNSS sites significantly reduces discrepancies between different satellites, constellations, and receivers, enhancing temporal and spatial consistency, with a standard deviation improvement of over 20%. The long-term stability of satellite DCBs shows tiny fluctuations for the Global Positioning System (GPS), GALILEO, and BeiDou Navigation Satellite System (BDS) systems within +/- 0.5 ns, with slightly larger fluctuations for the GLONASS system within +/- 0.6 ns. The long-term stability of receiver DCBs shows that the standard deviation in mid- and high-latitude regions ranges from 0.1 to 0.2 ns, while in low-latitude regions ranging from 0.3 to 0.6 ns. The proposed method leverages multi-GNSS big data and pronouncedly improves the accuracy of global ionospheric TEC and DCB estimation, which provides a valuable tool for high-precision global ionosphere monitoring and related applications.