Maternal and neonatal mortality and morbidity, particularly in developing countries, are high even in the twenty-first century, which is a cause for concern. Therefore, this paper examines the Continuum of Mother and Neonatal Health Care (MNH), i.e., at least four ante-natal care visits (ANC 4 +), skilled birth attendance at delivery (SBA), post-natal care (PNC), and its determinants in 10 developing countries in Asia. It uses Demographic and Household Survey data (2014–2021) and finds that only 46% of women received all the MNH services, and 8% did not receive any services. In Afghanistan, only 2.8% of women availed complete care of MNH services, followed by Timor-Leste (26.1%), Bangladesh (31.5%), Pakistan (35.1%), and Nepal (38.8%). Empirical analysis shows that women with higher education, those living in urban areas, from wealthy families, and female-headed households have higher odds of availing all MNH. Media exposure, ease of access to MNH services, and the women who have attended the first ANC at less than four months of pregnancy have higher odds of availing all three MNH services. Therefore, the MNH policy should target women in rural areas who have a lower level of education and come from low-income families to improve the mother and neonatal health situation in South and Southeast Asia.