Grid maps are widely established for the representation of static objects in robotics and automotive applications. Though, incorporating velocity information is still widely examined because of the increased complexity of dynamic grids concerning both velocity measurement models for radar sensors and the representation of velocity in a grid framework. In this paper, both issues are addressed: sensor models and an efficient grid framework, which are required to ensure efficient and robust environment perception with radar. To that, we introduce new inverse radar sensor models covering radar sensor artifacts such as measurement ambiguities to integrate automotive radar sensors for improved velocity estimation. Furthermore, we introduce UNIFY, a multiple belief Bayesian grid map framework for static occupancy and velocity estimation with independent layers. The proposed UNIFY framework utilizes a grid-cell-based layer to provide occupancy information and a particle-based velocity layer for motion state estimation in an autonomous vehicle's environment. Each UNIFY layer allows individual execution as well as simultaneous execution of both layers for optimal adaption to varying environments in autonomous driving applications. UNIFY was tested and evaluated in terms of plausibility and efficiency on a large real-world radar data-set in challenging traffic scenarios covering different densities in urban and rural sceneries.