Tackling malnutrition is a major health priority for a developing country like Bangladesh. This study explored the differences in prevalence of having only one form, and multiple forms, of severe malnutrition (stunting, wasting and underweight) among under-5 children in Bangladesh, and aimed to identify the important factors affecting these. Data were extracted from the Bangladesh Demographic Health Surveys conducted in 2007, 2011 and 2014. The outcome measures were ‘only one form’ and ‘multiple forms’ of severe malnutrition in children aged under 5 years. A Chi-squared test was performed to find the association of outcome variables with selected socio-demographic factors and logistic regression models were applied to identify risk factors. A total of 19,874 children aged under 5 years were included in the analysis. The overall proportion with one form of severe child malnutrition was approximately 12%, and the proportion with multiple forms was 8%. Age, mother’s education, father’s occupation, mother currently working, watching television, source of water, solid waste used in cooking, intimate partner violence (IPV), wealth index, urban/rural place of residence and birth cohort were found to be significant factors for both having only one and having multiple forms of severe child malnutrition. Children with an uneducated mother of poor socioeconomic class had a higher risk of severe malnutrition. Children of fathers with a professional occupation were at lower risk of having multiple forms of severe malnutrition. The proportions of children aged under 5 years with one or multiple forms of severe malnutrition were shown to be high in Bangladesh. The prevention of malnutrition in the country should be seen as a significant public health issue and given top priority.