Hybridizing species complexes provide one of the richest natural experiments in evolutionary biology. Interspecific hybridization can break up co-adapted genes, disrupt local adaptation and produce genomic extinction. But it could also be viewed as a creative force behind species formation, particularly at differing levels of gene flow in a so-called "mosaic of speciation". Here we explore the genomic consequences of introgressive hybridization in a hybridizing complex of closely related Darwin ground Finches. We identified more than 41,000 SNPs across the three sympatric species of ground finches (Geospiza fuliginosa, G. fortis, G. magnirostris), including the two distinct fortis morphs. We found that despite high levels of gene flow across all species, we could detect ~600 species-specific SNPs associated to "conventional" morphological categories, but no association was found when these SNPs where chosen randomly. These findings suggest genetic permeability across "porous" species boundaries where neutral loci can move freely but putative naturally selected loci get trapped. We suggest the importance of species bridges in creating and maintaining species identities and stress the important role of introgressive hybridization behind the radiation of Darwin’s Finches.