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Unemployment insurance (UI) is the primary safety net for workers experiencing involuntary job loss, yet its consequences for family life remain understudied relative to its labor market effects. When a parent loses a job, they gain time freed from work while facing tighter finances, heightened stress, and pressure to search for new employment. Whether more generous UI enables parents to direct freed time toward their children, by relaxing financial pressure and extending income support, is an open empirical question. This paper provides the first direct evidence on the relationship between UI benefit duration and parental time investment during unemployment. The analysis exploits variation in the maximum number of weeks of UI benefits across states and years as a continuous measure of UI generosity. This variation reflects both long-standing cross-state differences in program design and, importantly, within-state legislative changes: after the Great Recession, several states permanently cut maximum duration from the longstanding 26-week standard to as few as 12 weeks, while others maintained or modestly adjusted their programs. State and year fixed effects absorb time-invariant differences across states and common year-to-year trends. The empirical analysis draws on the American Time Use Survey linked to the Current Population Survey (2003 to 2019), restricted to unemployed parents aged 18 to 64 living with at least one child under 18. The sample period ends in 2019 to avoid contamination from pandemic-era federal UI expansions. Outcomes capture total time with children, primary childcare, enrichment time (reading, play, arts and crafts), and education-related time (homework help, school activities), along with job search time. Each additional week of potential UI benefits is associated with increases in enrichment and education-related caregiving, with effects concentrated among single parents, who also show reductions in job search time. This pattern is consistent with income support relaxing the urgency of immediate reemployment and allowing single parents to invest more deliberately in their children. Effects for cohabiting parents are more modest, suggesting within-household substitution across partners dampens the observable impact on individual parental time. These findings extend the UI literature beyond labor market outcomes and consumption smoothing to the caregiving behaviors that shape child development, and contribute to growing evidence that income support generosity shapes family wellbeing. As states vary widely in UI generosity and federal retrenchment pressure mounts, understanding these broader consequences is increasingly important for policy.