ABSTRACT High-level cognitive skill development relies on genetic and environmental factors, tied to brain structure and function. Inter-individual variability in language and music skills has been repeatedly associated with the structure of the auditory cortex: the shape, size and asymmetry of the transverse temporal gyrus (TTG) or gyri (TTGs). TTG is highly variable in shape and size, some individuals having one single gyrus (also referred to as Heschl’s gyrus, HG) while others presenting duplications (with a common stem or fully separated) or higher-order multiplications of TTG. Both genetic and environmental influences on children’s cognition, behavior, and brain can to some to degree be traced back to familial and parental factors. In the current study, using a unique MRI dataset of parents and children (135 individuals from 37 families), we ask whether the anatomy of the auditory cortex is related to reading skills, and whether there are intergenerational effects on TTG(s) anatomy. For this, we performed detailed, automatic segmentations of HG and of additional TTG(s), when present, extracting volume, surface area, thickness and shape of the gyri. We tested for relationships between these and reading skill, and assessed their degree of familial similarity and intergenerational transmission effects. We found that volume and area of all identified left TTG(s) combined was positively related to reading scores, both in children and adults. With respect to intergenerational similarities in the structure of the auditory cortex, we identified structural brain similarities for mother-child pairs of the 1st TTG (HG) (in terms of volume, area and thickness for the right HG, and shape for the left HG) and of the lateralization of all TTG(s) surface area for father-child pairs. Both the HG and TTG-lateralization findings were significantly more likely for parent-child dyads than for unrelated adult-child pairs. Furthermore, we established characteristics of parents’ TTG that are related to better reading abilities in children: fathers’ small left HG, and a small ratio of HG to planum temporale. Our results suggest intergenerational transmission of specific structural features of the auditory cortex (not directly linked to children’s reading outcomes); these may arise from genetics and/or from shared environment.