Compressive spectral imaging (CSI) is an advanced computational imaging approach to reconstruct the three-dimensional (3D) spatio-spectral data cube of a target scene through a single or a few snapshots. However, limited by the response range of the image detector, the existing CSI systems mostly work within narrow spectral bands, such as the visible or shortwave-infrared (SWIR) spectral band. The work band of the CSI system constrains the detection capacity for the targets under complex environments (such as rain, snow, haze, etc.). In addition, most of the current CSI prototypes lack engineering design for practical applications. This paper develops a novel, to the best of our knowledge, optical design scheme of a broadband CSI system with co-aperture coding to simultaneously realize visible multi-spectral imaging (10 channels) and SWIR super-resolution imaging (16×). The freeform surfaces are used to design the front-end reflective objective lens, thus significantly improving the image quality and spatial modulation precision of the system. By means of performance evaluation and tolerance analysis, excellent image quality and manufacturability of the proposed system are demonstrated.