Sequence-to-function neural networks learn cis-regulatory rules of many types of genomic data from DNA sequence. However, a key challenge is to interpret these models to relate the sequence rules to underlying biological processes. This task is especially difficult for complex genomic readouts such as MNase-seq, which maps nucleosome occupancy but is confounded by experimental bias. To overcome these limitations, we introduce pairwise influence by sequence attribution (PISA), an interpretation tool that combinatorially decodes which bases are responsible for the readout at a specific genomic coordinate. PISA visualizes the effects of transcription factor motifs, uncovers previously hidden motifs with complex contribution patterns, and reveals experimental biases of genomics assays. Integrated into a deep learning suite called BPReveal, PISA enables accurate MNase-seq nucleosome prediction models with reduced experimental bias, allowing the de novo discovery of motifs that mediate nucleosome positioning and the design of sequences with altered nucleosome configurations. These results show that PISA is a versatile tool that expands our ability to extract novel cis-regulatory sequence rules from genomics data, paving the way towards deciphering the cis-regulatory code.