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Background: Little is known about how disaster exposure interacts with household characteristics to influence mental health in Bangladesh. This study examined associations between household and disaster-related factors and the occurrence of mental disorders during and after climatic disasters in Bangladesh between 2015 and 2020. Methods: This cross-sectional study analyzed data from the 2021 Bangladesh Disaster-Related Statistics (BDRS), covering 125,952 households. The outcome was self-reported mental disorder during or after climatic disasters. Hierarchical Bayesian logistic regression models were used to examine associations, with adjusted odds ratios (ORs) and 95% credible intervals (CrIs) reported. Findings: Exposure to coastal erosion, landslides, or salinity (OR = 3.32; 95% CrI: 1.17–10.23) was associated with increased risk of mental disorder. Higher risk was also found in households headed by divorced/separated individuals (OR = 3.64; 95% CrI: 1.40–8.76), labourers (OR = 1.41; 95% CrI: 1.01–1.98), and unemployed persons (OR = 3.13; 95% CrI: 1.55–6.03). Households with a chronically ill member (OR = 3.48; 95% CrI: 2.36–5.10), malnourished child (OR = 5.17; 95% CrI: 3.14–8.35), or someone with disability (OR = 3.66; 95% CrI: 2.60–5.15) were at elevated risk. Agricultural/property loss (OR = 1.08; 95% CrI: 1.02–1.14) and housing damage (OR = 1.06; 95% CrI: 1.01–1.12) were linked to post-disaster mental disorders. Interpretation: Mental health support and social protection should be integrated into climate resilience planning, especially for socioeconomically disadvantaged households.