Sensory atypicalities are a common feature of autism spectrum disorder (ASD). To date, the relationship between sensory atypicalities in dyads of children with ASD and their parents has not been investigated. Exploring these relationships can contribute to an understanding of how phenotypic profiles may be inherited, and the extent to which familial factors might contribute towards children’s sensory profiles and constitute an aspect of the broader autism phenotype (BAP). Parents of 44 children with ASD and 30 typically developing (TD) children, aged between 3 and 14 years, participated. Information about children’s sensory experiences was collected through parent report using the Sensory Profile questionnaire. Information about parental sensory experiences was collected via self-report using the Adolescent/Adult Sensory Profile. Parents of children with ASD had significantly higher scores than parents of TD children in relation to low registration, over responsivity, and taste/smell sensory processing. Similar levels of agreement were obtained within ASD and TD parent-child dyads on a number of sensory atypicalities; nevertheless significant correlations were found between parents and children in ASD families but not TD dyads for sensation avoiding and auditory, visual, and vestibular sensory processing. The findings suggest that there are similarities in sensory processing profiles between parents and their children in both ASD and TD dyads. Familial sensory processing factors are likely to contribute towards the BAP. Further work is needed to explore genetic and environmental influences on the developmental pathways of the sensory atypicalities in ASD.