The regulation of gene expression in cells, including by microRNAs (miRNAs), is a dynamic process. Current methods for identifying miRNA targets by combining sequence and miRNA and mRNA expression data do not adequately use the temporal information and thus miss important miRNAs and their targets. We developed the MIRna Dynamic Regulatory Events Miner (mirDREM), a probabilistic modeling method that uses input-output hidden Markov models to reconstruct dynamic regulatory networks that explain how temporal gene expression is jointly regulated by miRNAs and transcription factors. We measured miRNA and mRNA expression for postnatal lung development in mice and used mirDREM to study the regulation of this process. The reconstructed dynamic network correctly identified known miRNAs and transcription factors. The method has also provided predictions about additional miRNAs regulating this process and the specific developmental phases they regulate, several of which were experimentally validated. Our analysis uncovered links between miRNAs involved in lung development and differentially expressed miRNAs in idiopathic pulmonary fibrosis patients, some of which we have experimentally validated using proliferation assays. These results indicate that some disease progression pathways in idiopathic pulmonary fibrosis may represent partial reversal of lung differentiation.