Analyses of the increasingly available genomic data continue to reveal the extent of hybridization and its role in the evolutionary diversification of various groups of species. We show, through extensive coalescent-based simulations of multi-locus data sets on phylogenetic networks, how divergence times before and after hybridization events can result in incomplete lineage sorting with gene tree incongruence signatures identical to those exhibited by hybridization. Evolutionary analysis of such data under the assumption of a species tree model can miss all hybridization events while analysis under the assumption of a species network model would grossly overestimate hybridization events. These issues necessitate a paradigm shift in evolutionary analysis under these scenarios, from a model that assumes a priori a single source of gene tree incongruence to one that integrates multiple sources in a unifying framework. We propose a framework of coalescence within the branches of a phylogenetic network, and show how this framework can be used to detect hybridization despite incomplete lineage sorting. We apply the model to simulated data, and show that the signature of hybridization can be revealed as long as the divergence times of the species involved in hybridization is not too small. We reanalyze a data set of 106 loci from 7 ingroup Saccharomyces species for which a species tree with no hybridization has been reported in the literature. Our analysis supports the hypothesis that that hybridization occurred during the evolution of this group, explaining a large amount of the incongruence in the data. Our findings show that an integrative approach to gene tree incongruence and its reconciliation is needed. Our framework will help in systematically analyzing genomic data for the occurrence of hybridization and elucidating its evolutionary role.