Forced displacement is a major driver of mental health disorders among refugees globally. The mental well-being of adult refugees, particularly mothers, is widely recognized as a crucial determinant of their children's psychological health and development. In this study, we conducted a randomized controlled trial (RCT) to examine the effectiveness of a multifaceted psychosocial program in improving the mental health of refugee mothers, and fostering growth and development among children under the age of two. Collaborating with BRAC, we conducted a cluster RCT involving 3,500 Rohingya mother-child pairs in refugee camps in Bangladesh. Participants received weekly psychosocial support for 44 weeks, facilitated by trained peer volunteers. The program included psychoeducation and parenting guidance for mothers, as well as interactive play activities for both mothers and children. The intervention proved largely successful, resulting in: (i) reductions in the psychological trauma and depression severity among both mothers and children, (ii) improvements in children's communication, gross-motor, and problem-solving skills, and (iii) reductions in the prevalence of stunting and severe stunting among children. At a cost of approximately $1 per dyad per session, the intervention has demonstrated cost-effectiveness and is currently being scaled-up in Bangladesh's refugee camps, benefiting around forty thousand mother-child dyads.