The mammalian placenta is a hotspot for the evolution of genomic imprinting, a form of gene regulation that involves the parent-specific epigenetic silencing of one allele. Imprinted genes are central to placental development and are thought to contribute to the evolution of reproductive barriers between species. However, it is unclear how rapidly imprinting evolves or how functional specialization among placental tissues influences the evolution of imprinted expression. We compared parent-of-origin expression bias across functionally distinct placental layers sampled from reciprocal crosses within three closely related lineages of mice Mus. Using genome-wide gene expression and DNA methylation data from fetal and maternal tissues, we developed an analytical strategy to minimize pervasive bias introduced by maternal contamination of placenta samples. We corroborated imprinted expression at 42 known imprinted genes and identified five candidate imprinted genes showing parent-of-origin specific expression and DNA methylation. Paternally-biased expression was enriched in the labyrinth zone, a layer specialized in nutrient transfer, and maternally-biased genes were enriched in the junctional zone, which specializes in modulation of maternal physiology. Differentially methylated regions were predominantly determined through epigenetic modification of the maternal genome and were associated with both maternally- and paternally-biased gene expression. Lastly, comparisons between lineages revealed a small set of co-regulated genes showing rapid divergence in expression levels and imprinted status in the M. m. domesticus lineage. Together, our results reveal important links between core functional elements of placental biology and the evolution of imprinted gene expression among closely related rodent species.