Cleft palate only is a common birth defect with high heritability. Only a small fraction of this heritability is explained by the genetic variants identified so far, underscoring the need to investigate other disease mechanisms, such as gene-environment (GxE) interactions and parent-of-origin (PoO) effects. Furthermore, PoO effects may vary across exposure levels (PoOxE effects). Such variation is the focus of this study. We upgraded the R-package Haplin to enable direct tests of PoOxE effects at the genome-wide level. From a previous GWAS, we had genotypes for 550 case-parent trios, of mainly European and Asian ancestry, and data on three maternal exposures (smoking, alcohol, and vitamins). Data were analyzed for Europeans and Asians separately, and also for all ethnicities combined. To account for multiple testing, a false discovery rate method was used, where q-values were generated from the p-values. In the Europeans-only analyses, interactions with maternal smoking yielded the lowest q-values. Two SNPs in the 'Interactor of little elongation complex ELL subunit 1' (ICE1) gene had a q-value of 0.14, and five of the 20 most significant SNPs were in the 'N-acetylated alpha-linked acidic dipeptidase-like 2' (NAALADL2) gene. No evidence of PoOxE effects was found in the other analyses. The connections to ICE1 and NAALADL2 are novel and warrant further investigation. More generally, the new methodology presented here is easily applicable to other traits and exposures in which a family-based study design has been implemented.