With advancements in the broadcast ephemeris accuracy of global navigation satellite systems (GNSSs), precise point positioning based on broadcast ephemeris (BE-PPP) is gradually showing promising prospects. However, the periodic updates of GNSS ephemeris result in discontinuities in the satellite orbit and clock offset during handovers. These discontinuities can significantly impact positioning accuracy. In this study, we calculate the combined ephemeris discontinuities, which indicate a linear combination of satellite radial orbit and clock discontinuities. We then compensate for the combined ephemeris discontinuities in the subsequent satellite clocks prior to positioning. For BeiDou Navigation Satellite System 3 (BDS-3) and the Global Positioning System (GPS), the three-dimensional (3D) position accuracy in kinematic mode is improved by 30–50 cm, reaching 33.9 cm. For GPS/Galileo/BDS-3 triple-constellation kinematic solutions, the accuracy reaches 23.2 cm. In static mode, the 3D position accuracy is 14.6 cm for BDS-3-only positioning and 15.1 cm for GPS. For GPS/Galileo/BDS-3 triple-constellation static BE-PPP solutions, the 3D position accuracy improves to 8 cm.