Search Models of the labor market are widespread and influential but they usually ignore that labor market decisions are frequently taken at the household level. We fill this gap by developing and estimating an household search model with on-the-job search and labor supply. We build on previous work (Dey and Flinn (2008) and Guler, Guvenen and Violante (2011)) to propose a novel identification strategy of the risk aversion parameters and a specification test. We find that ignoring the household as unit of decision-making has relevant empirical consequences. In estimation, the individual search specification implies gender wage offers differentials 200% larger than the household search specification. In the application, the individual search specification implies gender differentials in lifetime utility inequality 74% larger. The results of our policy experiments emphasize the importance of looking at lifetime utility inequality measures as opposed to simply cross-sectional wage inequality measures.