Compressive spectral imaging (CSI) captures multispectral imagery using fewer measurements than those required by traditional Shannon-Nyquist theory-based sensing procedures. CSI systems acquire coded and dispersed random projections of the scene rather than direct measurements of the voxels. To date, the coding procedure in CSI has been realized through the use of block-unblock coded apertures (CAs), commonly implemented as chrome-on-quartz photomasks. These apertures block or permit us to pass the entire spectrum from the scene at given spatial locations, thus modulating the spatial characteristics of the scene. This paper extends the framework of CSI by replacing the traditional block-unblock photomasks by patterned optical filter arrays, referred to as colored coded apertures (CCAs). These, in turn, allow the source to be modulated not only spatially but spectrally as well, entailing more powerful coding strategies. The proposed CCAs are synthesized through linear combinations of low-pass, high-pass, and bandpass filters, paired with binary pattern ensembles realized by a digital micromirror device. The optical forward model of the proposed CSI architecture is presented along with a proof-of-concept implementation, which achieves noticeable improvements in the quality of the reconstruction.