Acute respiratory infection (ARI) and diarrhoea are two major causes of child morbidity and mortality in Bangladesh. National and regional level prevalence of ARI and diarrhoea are calculated from nationwide surveys; however, prevalence at micro-level administrative units (say, district and sub-district) is not possible due to lack of sufficient data at those levels. In such a case, small area estimation (SAE) methods can be applied by combining survey data with census data. Using an SAE method for the dichotomous response variable, this study aims to estimate the proportions of under-5 children experienced with ARI and diarrhoea separately as well as either ARI or diarrhoea within a period of two-week preceding the survey. The ARI and diarrhoea data extracted from Bangladesh Demographic and Health Survey 2011 are used to develop a random effect logistic model for each of the indicators, and then the prevalence is estimated adapting the World Bank SAE approach for the dichotomous response variable using a 5% sample of the Census 2011. The estimated prevalence of each indicator significantly varied by district and sub-district (1.4-11.3% for diarrhoea, 2.2-11.8% for ARI and 4.3-16.5% for ARI/diarrhoea at sub-district level). In many sub-districts, the proportions are found double of the national level. District and sub-district levels spatial distributions of the indicators might help the policymakers to identify the vulnerable disaggregated and remote hotspots. Particularly, aid industries can provide effective interventions at the highly vulnerable spots to overcome the gaps between micro and macro level administrative units.