We are preparing to return humans to the Moon and setting the stage for exploration to Mars and beyond. However, it is unclear if long missions outside of low-Earth orbit can be accomplished with acceptable risk. The central objective of a new modeling project, the Earth-Moon-Mars Radiation Exposure Module (EMMREM), is to develop and validate a numerical module for characterizing time-dependent radiation exposure in the Earth-Moon-Mars and interplanetary space environments. EMMREM is being designed for broad use by researchers to predict radiation exposure by integrating over almost any incident particle distribution from interplanetary space. We detail here the overall structure of the EMMREM module and study the dose histories of the 2003 Halloween storm event and a June 2004 event. We show both the event histories measured at 1 AU and the evolution of these events at observer locations beyond 1 AU. The results are compared to observations at Ulysses. The model allows us to predict how the radiation environment evolves with radial distance from the Sun. The model comparison also suggests areas in which our understanding of the physics of particle propagation and energization needs to be improved to better forecast the radiation environment. Thus, we introduce the suite of EMMREM tools, which will be used to improve risk assessment models so that future human exploration missions can be adequately planned for.