The multispecies network coalescent (MSNC) is a stochastic process that captures how gene trees grow within the branches of a phylogenetic network. Coupling the MSNC with a stochastic mutational process that operates along the branches of the gene trees gives rise to a generative model of how multiple loci from within and across species evolve in the presence of both incomplete lineage sorting (ILS) and reticulation (e.g., hybridization). We report on a Bayesian method for sampling the parameters of this generative model, including the species phylogeny, gene trees, divergence times, and population sizes, from DNA sequences of multiple independent loci. We demonstrate the utility of our method by analyzing simulated data and reanalyzing three biological data sets. Our results demonstrate the significance of not only co-estimating species phylogenies and gene trees, but also accounting for reticulation and ILS simultaneously. In particular, we show that when gene flow occurs, our method accurately estimates the evolutionary histories, coalescence times, and divergence times. Tree inference methods, on the other hand, underestimate divergence times and overestimate coalescence times when the evolutionary history is reticulate. While the MSNC corresponds to an abstract model of “intermixture,” we study the performance of the model and method on simulated data generated under a gene flow model. We show that the method accurately infers the most recent time at which gene flow occurs. For genotype data, our method adopts a phasing procedure that integrates over all possible phasing of diploid genotypes, providing accurate estimates of divergence times and parameters. In contrast, the common practice random phasing would result in failure detection of intermixture events, inaccurate divergence times and population sizes, especially at low time scales, as demonstrate by our simulation results.