The global BeiDou Navigation Satellite System (BDS-3) and regional system (BDS-2) are transmitting signals on three or more frequencies, which brings more choices and practical potentials. To deeply integrate and fully utilize the BDS-2 and BDS-3 signals, this research is dedicated to the modeling and assessment of BDS-2/BDS-3 combined triple-frequency precise point positioning (PPP). Using ionosphere-free (IF) or uncombined (UC) observables, the three BDS-2/BDS-3 combined triple-frequency PPP models, named IF1213, IF123 and UC123 are developed. Particularly, new biases such as time delay bias (TDB) and inter-frequency bias (IFB) as well as the parameterizations are addressed. One-month observations from 16 Multi-GNSS Experiment (MGEX) stations located in and around the Asia-Pacific region are utilized to validate and compare the models. The results indicate that the three BDS-2/BDS-3 combined triple-frequency PPP models have the comparable performance and the third frequency makes a marginal contribution to positioning and tropospheric delay retrieval. The TDB should be carefully considered in BDS-2/BDS-3 combined PPP, especially for the IF123 model due to the larger absolute values of TDB. Meanwhile, the IFB derived from receiver uncalibrated code delay difference shows good stability in both short-term (intra-day) and long-term (inter-day) periods. In addition, demonstrated by triple-frequency PPP tests with one-month data from 47 global MGEX stations, the BDS-2/BDS-3 combined constellation allows for significantly improved convergence performance and positioning accuracy over the BDS-2-only constellation. The BDS-3 system has the ability to provide the precise positioning accuracy of 12.1/9.8/15.8 mm on a global scale after the convergence time of 23.0/13.2/24.7 min in east/north/up components.