This paper develops a complementarity formulation for a multi-user class, simultaneous route and departure time choice dynamic user equilibrium (DUE) model. A path-based multiclass cell transmission model (mCTM) is embedded to propagate the traffic flow on the network. Heterogeneous user classes are incorporated in the new formulation and heterogeneity is based on different preferred arrival times, cost perception for travel time, early and late arrival penalties. Multiple model properties have been showed. The proposed model is solved as an equivalent non-monotone variational inequality (VI) problem defined on a product set. A modified proximal point algorithm is used to solve the proposed non-monotone VI problem. Numerical results show that the solution approach is able to find the equilibrium or close to equilibrium solutions. The new formulation and solution approach show the feasibility of solving the multiclass DUE problem for general traffic networks.