There is a growing number of studies on the traffic control strategies of signal timings and vehicle trajectories at signalized intersections, while lane assignments are widely pre-specified and fixed. Meanwhile, existing strategies generally require a fully connected and automated vehicles (CAVs) environment. To fill up the gaps, this study contributes to a two-dimensional (spatiotemporal) control strategy by jointly optimizing traffic signals, lane settings, and vehicle trajectories at isolated signalized intersections under the mixed traffic of connected automated and human-driven vehicles. Specifically, based on the pseudo-platoons, signal timing plans and settings of approach lanes are jointly optimized by a piece-wise linear programming model. Then, vehicle trajectory control is integrated into the collaborative control framework to smooth vehicle trajectories. Three groups of numerical experiments are conducted to verify the effectiveness and efficiency of the proposed control method. Results show that the proposed algorithm outperforms the actuated control in terms of vehicle travel time under both under-saturated and over-saturated traffic conditions.