Family Economic Stimulus Act of 2008 - Amends the Internal Revenue Code to: (1) exclude unemployment compensation from gross income in 2007 and 2008; (2) increase the child tax credit to $1,200 in 2008; (3) allow individual taxpayers a $400 tax rebate ($800 in the case of a joint return) in 2008; (4) extend unemployment insurance benefits; and (5) require states to distribute to unemployed individuals information about unemployment insurance eligibility conditions.