With the worsening vehicle emissions, carbon emission charges are becoming an increasingly popular policy to reduce emissions. This paper proposes a policy to charge for the additional CO2 emissions due to the increasing traffic flow for each vehicle, thereby extending traditional travel time-based traffic assignment to emissions-charged traffic assignment. Considering that vehicle movements in the network are affected by signal timings and the car-following together with lanechanging interactions of different types of vehicles, microscopic traffic flow simulation is combined with a CO2 emission model to formulate the relations between link flow and emissions of different types of vehicles. Accordingly, the additional CO2 emissions due to increasing traffic flow are quantified and charged for each vehicle, leading to multi-vehicle-type and multi-criteria traffic assignment. Through an example network, the proposed flow-emissions model is verified and the impacts of different CO2 charging prices in the morning peak hour are investigated. Analysis of the results shows monotone increasing relations between price and reduced total emissions as well as increased revenue within the price range. In addition, the charging policy also leads to traffic assignment that achieves a system-optimal assignment since the CO2 pricing aligns with the general concept of pricing externality, thereby reducing the total travel time.