Tax Free Health Savings Act of 2006 - Amends the Internal Revenue Code to: (1) allow individual taxpayers a tax deduction for high deductible health plan premiums, a tax credit for employment taxes related to the payment of such premiums, and a refundable tax credit for the coverage costs under a high deductible health plan: (2) direct the Secretary of the Treasury to establish a program for advance payments of tax credit amounts to providers of high deductible health plans; (3) increase the tax deduction for contributions to health savings accounts; (4) allow health savings accounts to incorporate flexible spending arrangements or health reimbursement arrangements, or both; (5) allow payment of high deductible health plan premiums from health savings accounts; and (6) exempt employers from health savings account contribution requirements for certain employees with high levels of medical expenses.