We present generalizable and interpretable supervised deep learning frameworks to predict regulatory and epigenetic state of putative functional genomic elements by integrating raw DNA sequence with diverse chromatin assays such as ATAC-seq, DNase-seq or MNase-seq. First, we develop novel multi-channel, multi-modal CNNs that integrate DNA sequence and chromatin accessibity profiles (DNase-seq or ATAC-seq) to predict in-vivo binding sites of a diverse set of transcription factors (TF) across cell types with high accuracy. Our integrative models provide significant improvements over other state-of-the-art methods including recently published deep learning TF binding models. Next, we train multi-task, multi-modal deep CNNs to simultaneously predict multiple histone modifications and combinatorial chromatin state at regulatory elements by integrating DNA sequence, RNA-seq and ATAC-seq or a combination of DNase-seq and MNase-seq. Our models achieve high prediction accuracy even across cell-types revealing a fundamental predictive relationship between chromatin architecture and histone modifications. Finally, we develop DeepLIFT (Deep Linear Importance Feature Tracker), a novel interpretation engine for extracting predictive and biological meaningful patterns from deep neural networks (DNNs) for diverse genomic data types. DeepLIFT is the first method that can integrate the combined effects of multiple cooperating filters and compute importance scores accounting for redundant patterns. We apply DeepLIFT on our models to obtain unified TF sequence affinity models, infer high resolution point binding events of TFs, dissect regulatory sequence grammars involving homodimer and heterodimeric binding with co-factors, learn predictive chromatin architectural features and unravel the sequence and architectural heterogeneity of regulatory elements.