We examined the association between socioeconomic status (SES) and continuum of care (CoC) completion rate in maternal, neonatal, and child health among mothers in Bangladesh. We used data from the Bangladesh Demographic Health Survey (BDHS) from 2017 to 2018. Our findings were based on the responses of 1527 married women who had at least one child aged 12 to 23 months at the time of the survey. As a measure of SES, we focused on the standard of living (hereinafter referred to as wealth). The CoC for maternal and child health (MNCH) services is the study's outcome variable. The CoC was calculated using seven MNCH interventions: four or more antenatal care (ANC) visits with a skilled practitioner, delivery by a skilled birth attendant, post-natal care for mothers (PNCM) within two days of giving birth, post-natal care for newborns (PNCM) within two days of birth, immunization, age-appropriate breastfeeding, and maternal current use of modern family planning (FP) methods. Only 18.1% of Bangladeshi women completed all seven MNCH care interventions during the reproductive life span. Participants in the high SES group were 2.30 times (95% confidence interval [CI] 1.61–3.28) more likely than those in the low SES group to have higher composite care index (CCI) scores. Women with secondary or higher secondary education, as well as women who were exposed to mass media at least once a week, women who lived in an urban setting, women who had an intended pregnancy, and women with one parity, are associated with high CCI scores when other sociodemographic variables are considered. The complete CoC for MNCH reveals an extremely low completion rate, which may suggest that Bangladeshi mothers, newborns, and children are not receiving the most out of their present health care. Participants in the high SES group displayed higher CCI values than those in the low SES group, indicating that SES is one of the primary drivers of completion of CoC for MNCH services.