Linguistic alignment--the contingent reuse of our interlocutors' language at all levels of linguistic structure--pervades human dialogue. Here, we design unique measures to capture the degree of linguistic alignment between interlocutors' linguistic representations at three levels of structure: lexical, syntactic, and semantic. We track these measures in a longitudinal dataset of early conversations between caregivers and children with and without perinatal brain injury. Specifically, we test the predictions of the well-known Interactive Alignment Model, taking advantage of the variability within our sample in terms of the strength of interlocutors' linguistic representations, whether owed to age or injury. Ultimately, we find inconsistent support for the (largely untested) predictions of the Interactive Alignment Model, pointing to a need for new quantitative accounts of the mechanisms underlying linguistic alignment. Our results regarding the trajectory of interactive alignment broadly replicate developmental trends documented by other researchers, though analyses linking concurrent vocabulary and child alignment, as well as caregiver alignment and later child vocabulary--defy predictions from previous work. Our goal with these analyses is to start a conversation regarding the mechanisms underlying linguistic alignment, and to inform theories of how interactive linguistic experience supports language development.