Parental bonding to their infant is important for healthy parent-infant interaction and infant development. Characteristics in the parents affect how they bond to their newborn. Parental cognitions such as repetitive negative thinking, a thinking style associated with mental health issues, and cognitive dispositions, e.g., mood-congruent attentional bias or negative implicit attitudes to infants, might affect bonding. To assess the influence of cognitive factors on bonding, 350 participants (220 pregnant women and their partners) were recruited over two years by midwives at the hospital and in the communal health care services. Participants were followed throughout the pregnancy and until the infant was seven months old as a part of the Northern Babies Longitudinal Study. Both mothers and fathers took part. First, we measured demographics, repetitive negative thinking, attentional bias, and implicit attitudes to infants during pregnancy, as predictors of bonding two months postnatally. Second, we also measured infant regulatory problems, and depressive symptoms at two months postnatally as predictors of parents' perception of infant temperament at five months. Robust regression analyses were performed to test hypotheses. Results showed that mothers and fathers differed on several variables. Parity was beneficial for bonding in mothers but not for fathers. Higher levels of mothers' repetitive negative thinking during pregnancy predicted weaker bonding, which was a non-significant trend in fathers. For fathers, higher education predicted weaker bonding, but not for mothers. Mothers' perception of their infant temperament at five months was significantly affected by bonding at two months, but for fathers, their depressive symptoms were the only significant predictor of perceived infant temperament. In conclusion, for mothers, their relationship with their infant is essential for how they experience their infant, while for fathers their own wellbeing might be the most important factor. Health care providers should screen parents' thoughts and emotions already during pregnancy to help facilitate optimal bonding.