Motor vehicle crashes are a leading cause of death and injury for children aged under 8 years. In the U.S.A., while some states are showing increases in the proportion of child restraint device use, only around half of child passengers aged from 4 to 7 years are being properly restrained. This study was undertaken to identify the factors contributing to the proper child restraint use and child passenger’s seating position through the direct observation surveys of more than 10,000 child passengers in 2015 and 2018 in Michigan. A bivariate probit model with random effects was developed to identify simultaneously the contributing factors for the proper restraint use and seating position of child passengers, accounting for the unobserved heterogeneity in the data. The bivariate framework is able to account for the correlation of the two dependent variables in the study. The results show that the two dependent variables are positively correlated, and this correlation is strongly significant. The key factors simultaneously influencing proper child restraint use and appropriate seating position of the child passenger include the age of the child, the number of child passengers in the vehicle, driver belt use, driver gender, age, and race, vehicle type, stratum, weather, and the time of the day and week. However, factors such as county-specific population, income, and education, and the type of location did not have any significant association with either child restraint use or the seating position of the child passenger.