The current study examined the inter-brain coherence (IBC) between 34 dyads of fathers and infants 7-9 months of age using functional near-infrared spectroscopy (fNIRS). We specifically focused on father-infant IBC to broaden the empirical base beyond the mother-infant connections, as the former has received limited attention. There were three conditions: a baseline condition and two task conditions when the infant and the adult participant jointly listened to maternal storytelling in Cantonese in infant-directed speech (IDS) and adult-directed speech (ADS). Father-infant IBC was compared with stranger-infant IBC in the same experimental settings. Our results found that father-infant IBC was greater in the baseline and ADS conditions but not in the IDS condition, compared to stranger-infant IBC. Further, stranger-infant dyads showed greater IBC in the IDS condition than in the ADS condition, with no significance in father-infant IBC between the two speech conditions. These results identified different inter-brain connection mechanisms between the two dyads. The IBC pattern in stranger-infant dyads is driven by neural entrainment to mothers' speech, whereas father-infant IBC is more resistant to mothers' behaviours in the co-presence of both parents.