Prosody in infant-directed speech (IDS) serves important functions for the infant's attention, regulation, and emotional expression. However, how the structural characteristics of this vocal signal are influenced by the presence or absence of one or two parents at different infant ages remains under-investigated. This study aimed to identify the acoustic characteristics of parental vocalizations in 69 families during specific phases of the Lausanne Trilogue Play (LTP) setting. Vocalizations were analyzed in both two-person contexts (mother-baby or father-baby interacting with the infant individually) and three-person contexts (mother-baby or father-baby interactions in the presence of the other parent) at three time points: when the infant was 3, 9, and 18 months old. Videos of interactions were coded, and the parental vocalizations were extracted. Five components of acoustic features related to the prosodic aspects of speech were extracted for subsequent analysis: intensity and its variability, pitch and pitch variability, formant amplitude, the intensity of specific speech frequency bands affecting sound timbre, and the rate of voiced and unvoiced segments per second. The study demonstrated a main effect of infant age on parental acoustic prosodic characteristics, along with significant interactions between infant age and interaction context (two- versus three-person) and between infant age and parental role (mother versus father). Across contexts and parental roles, intensity, pitch, and their variability consistently increased from 3 to 9 months. By 9 months, distinct prosodic patterns emerged, including a reduced syllable rate and formant amplitude, along with an increase in pauses. The mother's voice exhibited a steady increase in intensity, as well as in pitch and intensity variability. Interestingly, when comparing parents across the two contexts, IDS in the three-person context is characterized by a higher rate of syllables and fewer pauses, with the most pronounced changes observed at 9 months of age. The development of prosodic characteristics in IDS is not constant across age and it is influenced by the complex interactions between age phases, parental gender, and contextual factors, with a dynamic adaptation of the communication strategies in three-person contexts. The current study underscores the importance of taking a comprehensive perspective in analyzing infant-directed speech within an interactive context involving both fathers and mothers in two- and three-person settings.