Animals communicating through acoustic signaling may compete for “acoustic space”. In tropical rainforests, birds and insects are the most acoustically active animals during the daytime, and insects are considered a major source of noise for singing birds. However, the extent to which birds and insects partition acoustic space in tropical forests is poorly known. We analyzed bird and insect acoustic activity at different time scales using passive acoustic monitoring data collected over a year in southern Vietnam. Recordings were made for 5 min every 25 min over 24-h periods, which allowed us to investigate temporal dynamics at daily and seasonal scales. We first calculated acoustic indices for all 5-min recordings across the full dataset. To assess finer-scale interactions, we also sampled 100 recordings representing various times of day and seasons. Then, we assessed the elements of the soundscape (biophony, geophony, and anthropophony) in each recording. Insects and birds were the main elements of the daytime biophony, with insect sounds being most prominent. Insects were active both day and night, but their activity decreased at dawn, when bird activity peaked. We found no negative relationship between insect and bird sound occurrences in the selected recordings, suggesting that birds do not avoid periods of insect activity. Instead, the observed patterns likely reflect distinct circadian rhythms. Furthermore, insects calling at the same frequencies as birds usually do not produce sounds actively at dawn, when birds are the most active. This may contribute to increased acoustic partitioning between birds and insects.