The combined burden of stunting and wasting in children under five years is a serious public health concern. The present study aimed to estimate the joint burden of stunting and wasting among children aged 6–59 months and explore its spatial variation across Nepal. The 2016 Nepal Demographic and Health Survey data was used to study acute and chronic childhood malnutrition. A Bayesian distributional bivariate probit geoadditive model was designed to study the linear association and geographical variation of stunting and wasting among 6–59 months, children. Child-related factors such as low birth weight, fever in the last 2 weeks preceding the survey and fourth or greater birth order were associated with a higher likelihood of stunting. The likelihood of a child being stunted was significantly less in the wealthiest households, having improved toilet facilities, and if mothers were overweight. Children from severely food insecure households were significantly more likely, and children from poorer households were significantly less likely to suffer both acute and chronic malnutrition simultaneously. Results from spatial effect showed that children from Lumbini and Karnali had a higher burden of stunting, and the likelihood that achild would have been wasted was significantly higher in Madhesh and Province 1. Immediate nutritional efforts are vital in low-income and severely food insecure households to lessen the risk of stunting and wasting in under children. Disproportionate geographic variations in stunting and wasting warrant sub-regional-specific nutrition intervention to achieve nutrition targets and reduce the burden of childhood malnutrition across the country.