The Coded Aperture Snapshot Spectral Imaging (CASSI) system captures the three-dimensional (3D) spatio-spectral information of a scene using a set of two-dimensional (2D) random-coded Focal Plane Array (FPA) measurements. A compressive sensing reconstruction algorithm is then used to recover the underlying spatio-spectral 3D data cube. The quality of the reconstructed spectral images depends exclusively on the CASSI sensing matrix, which is determined by the structure of a set of random coded apertures. In this paper, the CASSI system is generalized by developing a multiple-aperture optical imaging system such that spectral resolution enhancement is attainable. In the proposed system, a pair of high-resolution coded apertures is introduced into the CASSI system, allowing it to encode both spatial and spectral characteristics of the hyperspectral image. This approach allows the reconstruction of superresolved hyperspectral data cubes, where the number of spectral bands is significantly increased and the quality in the spatial domain is greatly improved. Extensively simulated experiments show a gain in the peak-signal-to-noise ratio (PSNR), along with a better fit of the reconstructed spectral signatures to the original spectral data.