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Bayesian networks (BNs) are suitable models for studying complex interdependencies between multiple health outcomes, simultaneously. However, these models fail the assumption of independent observation in the case of hierarchical data. Therefore, this study proposes a two and three-level random intercept multilevel Bayesian network (MBN) models to study the conditional dependencies between multiple outcomes. The structure of MBN was learned using the connected three parent set block Gibbs sampler, where each local network was included based on Bayesian information criteria (BIC) score of multilevel regression. These models were examined using simulated data assuming features of both multilevel models and BNs. The estimated area under the receiver operating characteristics for both models were above 0.8, indicating good fit. The MBN was then applied to real child morbidity data from the 2016 Ethiopian Demographic Health Survey (EDHS). The result shows a complex causal dependencies between malnutrition indicators and child morbidities such as anemia, acute respiratory infection (ARI) and diarrhea. According to this result, families and health professionals should give special attention to children who suffer from malnutrition and also have one of these illnesses, as the co-occurrence of both can worsen the health of a child. • MBN is suitable to analyze multiple outcomes in multilevel data setting. • Two and three-level MBN was implemented using c3pb. • Model evaluation was done using the AUPRC and the AUCROC. • MBN demonstrates its applicability for addressing complex health challenges. [ABSTRACT FROM AUTHOR]