Electrified drive systems and eco-driving technologies play a crucial role in promoting energy conservation. Eco-driving for hybrid electric vehicles(HEVs) is an intricate problem involving intertwined speed planning and energy management. In this context, an ecological adaptive cruise control (eco-ACC) and powertrain energy management strategy considering Signal Phase Timing Message (SPaT) can enhance both performance and real-time implementation. Specifically, this study develops a novel co-optimization method based on Pontryagin's minimum principle (PMP) that combines car-following control rules with the SPaT for a parallel HEV. The methodology involves the following steps: firstly, the parallel HEV model is established; secondly, the safe following distance model is constructed and the car-following control rules are devised to ensure safe driving. Subsequently, the co-optimization method based on PMP is then presented to simultaneously optimize the eco-driving problem of an ego-vehicle by converting the inter-vehicle distance constraint of the lead-vehicle into the limitation of the speed of the ego-vehicle. Finally, simulations are conducted under different scenarios for both fused SPaT and non-fused SPaT strategy. The simulation results demonstrate a reduction in fuel consumption by 6.27% and 5.69% in two different scenarios, respectively, and a shorter driving time for the fused SPaT strategy compared to the non-fused SPaT strategy.