In this paper, we propose a parametric optimization approach to simultaneously determining trip distribution, mode choice, and user-equilibrium assignment. In our model, mode choice decisions are based on a binomial logit model and passenger and cargo demands are divided into appropriate mode according to the user equilibrium minimum travel time. Underlying network consists of road and rail networks combined and mode choice available is auto, bus, truck, passenger rail, and cargo rail. We provide an equivalent convex optimization problem formulation and efficient algorithm for solving this problem. The proposed algorithm was applied to a large scale network examples derived from the National Intermodal Transportation Plan (2000-2019).