Prior research on parenthood effects has typically used single-sex models and estimated average effects. By contrast, we estimate population-level variability in partners' changes in housework hours, paid work hours, occupation traits, and wages after becoming parents, and we explore whether one partner's adjustment offsets or supplements the other's. We find tradeoffs between spouses on paid work adjustments to parenthood, but complementarity in adjustments to housework hours, occupation traits, and wages. The effect of parenthood on wives' behaviors is larger and more variable than on husbands' behaviors in every domain. The modest variation between husbands in work responses to parenthood explains little of the variation in the motherhood penalty, while variation in wives' own behaviors plays a larger role. We refer to this pattern as tethered autonomy: variation across American couples in work responses to parenthood is shaped primarily by variation in wives' adjustments, while husbands' work acts largely as a fixed point.