Common-aperture active and passive hyperspectral three-dimensional imaging technology is a new remote sensing detection method, which combines active LiDAR and passive hyperspectral cameras in a single framework with shared optical systems. Thus, the difficulty of heterogeneous data registration is reduced, and the generation of the 3D spectral image by real-time fusion becomes possible. The real-time 3D imaging is characterized by data-intensiveness and computing-intensiveness, and the software and hardware co-design framework for system-on-a-programmable-chip provides a feasible solution to it. At present, the hardware/software partitioning is mostly derived from qualitative and empirical analysis, and it is challenging to achieve a quantitative and optimal design. A system-on-a-programmable-chip processing framework using a multi-objective programming model based on object weight was proposed to tackle this problem. In this processing framework, the graph-theory-based model with Ncut criterion was used to achieve high cohesion and low coupling functional modules partitioning. Then, the performances of functional modules with software fulfilment and hardware fulfilment were thoroughly analyzed and evaluated. Finally, aiming at the design requirement, the proposed multi-objective programming model was used for the hardware/software partitioning scheme. Two optimal hardware/software partitioning schemes based on the speed-first criterion or the power-first criterion were solved quantitatively for different scenarios. The result shows that the speed-first design overperforms an empirical design with an increase of 43.4% in processing speed, a reduction of 53.5% in power consumption.