Child mortality is an important indicator of child health and overall national development. Under-five mortality is unacceptably high in Low- and Middle-Income Countries (LMICs) including Bangladesh. Increased availability and access to the healthcare services can play a significant role to reduce under-five mortality. The aim of this study was to explore the associations of several forms of child mortality with health facility level factors. Data were extracted from the 2017-18 Bangladesh Demographic and Health Survey data and 2017 Bangladesh Health Facility Survey data. Three outcome variables were considered: neonatal mortality, infant mortality, and under-five mortality in this study. Health facility level factors were considered as major explanatory variables. They were the availability of the child healthcare services at the nearest healthcare facility, readiness of the nearest healthcare facility to provide child healthcare services and the average distance of the nearest healthcare facility providing child healthcare services. Multilevel mixed-effect logistic regression model was used to determine the associations between the outcome variables and explanatory variables adjusted for covariates. We reported under-five, infant and neonatal mortality were 40, 37, and 30 per 1000 live births, respectively. The likelihood of neonatal and infant mortality was found to be declined for one-unit increase on the availability and readiness of the mothers’ homes nearest healthcare facilities to provide child healthcare services. On contrary, for every kilometre increased distance between mothers’ homes and their nearest healthcare facility was found to be associated with increased in the likelihoods of neonatal, infant and under-five mortality. The availability of health facilities providing child healthcare services close to residence and their improved management, infrastructure, and readiness to provide child healthcare services play a significant role in reducing under-five mortality in Bangladesh. Policies and programs should prioritize to increase the availability and accessibility of health facilities that provide child healthcare services.