When studying the vibration of a bridge-vehicle coupled system, most researchers mainly focus on the vertical vibration of bridges under moving vehicular loads, while the lateral and longitudinal vibrations of the bridges and the stochastic characteristics of the traffic flows are neglected. However, for long-span suspension bridges, neglecting the bridge's three-dimensional (3D) vibrations under stochastic traffic flows can cause considerable inaccuracy in predicting the dynamic performance. This study is mainly focused on establishing a new methodology fully considering a suspension bridge's vertical, lateral, and longitudinal vibrations induced by stochastic traffic flows under varied road roughness conditions. A new full-scale vehicle model with 18 degrees of freedom (DOFs) was developed to predict the longitudinal and lateral vibrations of the vehicle. An improved Cellular Automaton (CA) model considering the influence of the next-nearest vehicle was introduced. The bridge and vehicles in traffic flow coupled equations are established by combining the equations of motion of both the bridge and vehicles using the displacement relationship and interaction force relationship at the patch contacts. The numerical simulations show that the proposed method can rationally simulate the 3D vibrations of the suspension bridge under stochastic traffic flows.