Despite general agreement that laughter is crucial in social interactions and cognitive development, there is surprisingly little work looking at its use through childhood. Here we investigate laughter in middle childhood, using a corpus of online calls between child and parent and between the (same parent) and another adult. We focus on laughter mimicry, i.e., laughter shortly following laughter from the partner, and we compare mimicking and non-mimicking laughter in terms of distribution and acoustic properties using spectrotemporal modulation measures. Our results show, despite similar frequencies in laughter production, different laughter mimicry patterns between Parent-Child and Parent-Adult interactions. Overall, in comparison with previous work in infants and toddlers, our results show laughter mimicry is more balanced between parents and school-age children. At the acoustic level, we observe differences between mimicking and non-mimicking laughter in children, but not in adults. Moreover, we observe significant differences in laughter acoustics in parents depending on whether they interact with children or adults, which highlights a strong interlocutor effect on laughter mimicry.