As part of the 2030 maternal and child health targets, Ethiopia strives for universal and equitable use of health services. We aimed to examine the association between household wealth, maternal education, and the interplay between these in utilization of maternal and child health services. Data emanating from the evaluation of the Optimizing of Health Extension Program intervention. Women in the reproductive age of 15 to 49 years and children aged 12-23 months were included in the study. We used logistic regression with marginal effects to examine the association between household wealth, women's educational level, four or more antenatal care visits, skilled assistance at delivery, and full immunization of children. Further, we analyzed the interactions between household wealth and education on these outcomes. Household wealth was positively associated with skilled assistance at delivery and full child immunization. Women's education had a positive association only with skilled assistance at delivery. Educated women had skilled attendance at delivery, especially in the better-off households. Our results show the importance of poverty alleviation and girls' education for universal health coverage.