Mothers and children in families with one immigrant parent have been reported to be healthier than those in native families; however, the health of the fathers in these families has rarely been discussed in literature. We aimed to comprehensively compare the health of all the family members between families with one immigrant parent (native fathers, immigrant mothers, and their children) and native families (native fathers, native mothers, and their children). We conducted a cohort study by using the Taiwan Maternal and Child Health Database to recruit live-born children and their parents from 2004 to 2016. Overall, we identified 90,670 fathers, 91,270 mothers, and 132,457 children in families with one immigrant parent and 1,666,775 fathers, 1,734,104 mothers, and 2,637,191 children in native families and followed up with them from 2004 to 2017. The outcomes comprised common physical and mental disorders, catastrophic illnesses, mortality, and child adversities and accidents. The covariates comprised the child's year of birth, parental age, low-income status, and physical or mental disorder status. Logistic regression was performed to compare the risks of the outcomes between families with one immigrant parent and native families. The parents in families with one immigrant parent were more likely to be of low-income status and were older than the parents in native families. After adjusting for the covariates, fathers in families with one immigrant parent were found to have higher risks of physical and mental disorders, catastrophic illness, and mortality than fathers in native families. Conversely, mothers in families with one immigrant parent had lower risks of physical and mental disorders, catastrophic illness, and mortality than mothers in native families. Finally, the children in families with one immigrant parent generally had better physical and mental health but higher risks for leukemia, liver diseases, autism spectrum disorder, and road traffic accidents than children in native families. The health status of the members of families with one immigrant parent was nonhomogeneous, and the poorer general health of fathers in such families suggests health inequalities in families with one immigrant parent.