A significant fraction of the labor force consists of employed workers who are part-time unemployed (underemployed) in the sense that they are unable to work as much as they prefer. This paper develops a search and matching model to study the design of optimal unemployment insurance in an economy with unemployment as well as part-time unemployment. Part-time unemployment provides income insurance and serves as a stepping stone to full-time jobs. Unemployment benefits for part-timers increase the outflow from unemployment to part-time work but reduce the outflow from part-time work to fulltime employment. We examine the optimal structure of benefits for unemployed and underemployed workers. The results indicate non-negligible welfare gains associated with time limits for unemployment benefits as well as for part-time benefits. The welfare gains from optimal UI are larger when wages are fixed than when they are flexible.