Responsible Investment for Home Ownership Act of 2008 - Amends the Internal Revenue Code to: (1) establish tax-exempt Home Ownership Mortgage Expense Accounts; (2) allow a tax deduction for contributions to such accounts; (3) allow tax-free distributions from such accounts for the financing or remodeling of a principal residence; and (4) set forth rules for such accounts relating to prohibited transactions, rollover contributions, and account termination. Prohibits illegal aliens making tax deductible contributions to such accounts.