Light-scattering spectroscopy (LSS) is an established optical approach for nondestructive characterization of biological tissues. Here, we investigated the capabilities of LSS and convolutional neural networks (CNNs) to quantitatively characterize the composition and arrangement of cardiac tissues. We assembled tissue constructs from 200 μm thick sections of fixed myocardium and aortic wall. Thickness of the tissue constructs was similar to the thickness of atrial free wall. In the assembled constructs, the aortic sections represented fibrotic tissue and the depth, volume fraction, and arrangement of these fibrotic insets were varied. We gathered spectra with wavelengths from 500-1100 nm from the constructs at multiple locations relative to a light source. We used single and combinations of two spectra for training of CNNs. With independently measured spectra, we assessed the accuracy of the trained CNNs for classification of tissue constructs from single spectra and combined spectra. In general, classification accuracy with single spectra was smaller than with combined spectra. Combined spectra including spectra from fibers distal from the illumination fiber typically yielded a higher accuracy than proximal single collection fibers. Maximal classification accuracy of depth detection, volume fraction and permutated arrangements was (mean±stddev) 88.97±2.49%, 76.33±1.51% and 84.25±1.88%, respectively. Our studies demonstrate the reliability of quantitative characterization of tissue composition and arrangements using a combination of LSS and CNNs. Potential clinical applications of the developed approach include intraoperative quantification and mapping of atrial fibrosis as well as assessment of ablation lesions.