Stress resilience in parenting depends on the parent's capacity to understand subjective experiences in self and child, namely intersubjectivity, which is intimately related to mimicking other's affective expressions (i. e., mirroring). Stress can worsen parenting by potentiating problems that can impair intersubjectivity, e.g., problems of “over-mentalizing” (misattribution of the child's behaviors) and “under-coupling” (inadequate child-oriented mirroring). Previously we have developed Mom Power (MP) parenting intervention to promote maternal intersubjectivity and reduce parenting stress. This study aimed to elucidate neural mechanisms underlying the effects of MP with a novel Child Face Mirroring Task (CFMT) in functional magnetic-resonance-imaging settings. In CFMT, the participants responded to own and other's child's facial pictures in three task conditions: (1) empathic mirroring (Join), (2) non-mirroring observing (Observe), and (3) voluntary responding (React). In each condition, each child's neutral, ambiguous, distressed, and joyful expressions were repeatedly displayed. We examined the CFMT-related neural responses in a sample of healthy mothers (n = 45) in Study 1, and MP effects on CFMT with a pre-intervention (T1) and post-intervention (T2) design in two groups, MP (n = 19) and Control (n = 17), in Study 2. We found that, from T1 to T2, MP (vs. Control) decreased parenting stress, decreased dorsomedial prefrontal cortex (dmPFC) during own-child-specific voluntary responding (React to Own vs. Other's Child), and increased activity in the frontoparietal cortices, midbrain, nucleus accumbens, and amygdala during own-child-specific empathic mirroring (Join vs. Observe of Own vs. Other's Child). We identified that MP effects on parenting stress were potentially mediated by T1-to-T2 changes in: (1) the left superior-temporal-gyrus differential responses in the contrast of Join vs. Observe of own (vs. other's) child, (2) the dmPFC-PAG (periaqueductal gray) differential functional connectivity in the same contrast, and (3) the left amygdala differential responses in the contrast of Join vs. Observe of own (vs. other's) child's joyful vs. distressed expressions. We discussed these results in support of the notion that MP reduces parenting stress via changing neural activities related to the problems of “over-mentalizing” and “under-coupling.” Additionally, we discussed theoretical relationships between parenting stress and intersubjectivity in a novel dyadic active inference framework in a two-agent system to guide future research.