Household air pollution (HAP) from cooking with solid fuels has become a leading cause of death and disability in many developing countries including Bangladesh. We assess the association between HAP and risk of selected adverse birth and maternal health outcomes. Data for this study were extracted from Bangladesh Demographic and Health Survey conducted during 2007-2014. Selected adverse birth outcomes were acute respiratory infection (ARI) among children, stillbirth, low birth weight (LBW), under-five mortality, neonatal mortality and infant mortality. Maternal pregnancy complications and cesarean delivery were considered as the adverse maternal health outcomes. Place of cooking, use of solid fuel within the house boundary and in living room were the exposure variables. To examine the association between exposure and outcome variables, we used a series of multiple logistic regression models accounted for complex survey design. Around 90% of the respondents used solid fuel within the house boundary, 11% of them used solid fuel within the living room. Results of multiple regression indicated that cooking inside the house increased the risk of neonatal mortality (aOR,1.25; 95% CI, 1.02-1.52), infant mortality (aOR, 1.18; 95% CI, 1.00-1.40), ARI (aOR, 1.18; 95% CI, 1.08-1.33), LBW (aOR, 1.25; 95% CI, 1.10-1.43), and cesarean delivery (aOR,1.18; 95% CI, 1.01-1.29). Use of solid fuel, irrespective of cooking places, increased the risk of pregnancy complications (aOR, 1.36; 95% CI, 1.19-1.55). Compared to participants who reported cooking outside the house, the risk of ARI, LBW were significantly high among those who performed cooking within the house, irrespective of type of cooking fuel. Indoor cooking and use of solid fuel in household increase the risk of ARI, LBW, cesarean delivery, and pregnancy complication. These relationships need further investigation using more direct measures of smoke exposure and clinical measures of health outcomes. The use of clean fuels and structural improvement in household design such as provision of stove ventilation should be encouraged to reduce such adverse health consequences. Data related to health were collected by following the guidelines of ICF international and Bangladesh Medical Research Council. The registration number of data collection was 132,989.0.000, and the data-request was registered on March 11, 2015.