Schistosoma mansoni is a parasitic platyhelminth responsible for intestinal bilharzia. It has a complex life cycle, infecting a freshwater snail of the Biomphalaria genus, and then a mammalian host. Schistosoma mansoni adapts rapidly to new (allopatric) strains of its intermediate host. To study the importance of epimutations in this process, we infected sympatric and allopatric mollusc strains with parasite clones. ChIP-Seq was carried out on four histone modifications (H3K4me3, H3K27me3, H3K27ac and H4K20me1) in parallel with genomewide DNA resequencing (i) on parasite larvae shed by the infected snails and (ii) on adult worms that had developed from the larvae. No change in single nucleotide polymorphisms and no mobilization of transposable elements were observed, but 58-105 copy number variations (CNVs) within the parasite clones in different molluscs were detected. We also observed that the allopatric environment induces three types of chromatin structure changes: (i) host-induced changes on larvae epigenomes in 51 regions of the genome that are independent of the parasites' genetic background, (ii) spontaneous changes (not related to experimental condition or genotype of the parasite) at 64 locations and (iii) 64 chromatin structure differences dependent on the parasite genotype. Up to 45% of the spontaneous, but none of the host-induced chromatin structure changes were transmitted to adults. In our model, the environment induces epigenetic changes at specific loci but only spontaneous epimutations are mitotically heritable and have therefore the potential to contribute to transgenerational inheritance. We also show that CNVs are the only source of genetic variation and occur at the same order of magnitude as epimutations.