The Explicit Planetary Isentropic Coordinate (EPIC) atmospheric model has been upgraded to use a hybrid vertical coordinate that transitions continuously from potential temperature aloft to a function of a pressure-based sigma coordinate that is terrain following near topography. The result is a model that simulates terrestrial and gas-giant atmospheres equally well. Considering that surface pressure varies by orders of magnitude from one planet to the next whereas topography has a roughly similar geometric scale everywhere, we define the sigma coordinate in terms of log pressure rather than the traditional pressure. We include a pure-sigma region at the bottom that allows for accurate modeling of the planetary boundary layer (PBL) for terrestrial applications and the deep atmosphere for gas-giant applications. We describe the functional form for hybrid vertical coordinate in terms of potential temperature and sigma, the method used to calculate potential temperature, and the method used to calculate the hybrid vertical velocity, all of which are new. Potential temperature is only predicted in the pure-sigma region, while in the hybrid region it is found diagnostically; in a complementary manner, pressure is predicted in the hybrid region and at the surface but found diagnostically in the pure-sigma region. The hybrid vertical velocity, is calculated directly near the beginning of each timestep rather than iteratively at the end. A brief description of the model’s new turbulence scheme is included. To compare with previous models and to illustrate the flexibility of the hybrid coordinate, we run the Held-Suarez benchmark for Earth and a published Great Dark Spot simulation for Neptune.