Human respiratory syncytial virus (hRSV) affects more than 33 million people each year, but there are currently no effective drugs or vaccines approved. In this study, we first constructed a candidate host–pathogen interspecies genome-wide genetic and epigenetic network (HPI-GWGEN) via big-data mining. Then, we employed reversed dynamic methods via two-side host–pathogen RNA-seq time-profile data to prune false positives in candidate HPI-GWGEN to obtain the real HPI-GWGEN. With the aid of principal-network projection and the annotation of KEGG pathways, we can extract core signaling pathways during hRSV infection to investigate the pathogenic mechanism of hRSV infection and select the corresponding significant biomarkers as drug targets, i.e., TRAF6, STAT3, IRF3, TYK2, and MAVS. Finally, in order to discover potential molecular drugs, we trained a DNN-based DTI model by drug–target interaction databases to predict candidate molecular drugs for these drug targets. After screening these candidate molecular drugs by three drug design specifications simultaneously, i.e., regulation ability, sensitivity, and toxicity. We finally selected acitretin, RS-67333, and phenformin to combine as a potential multimolecule drug for the therapeutic treatment of hRSV infection.