Healthy Start Act of 1996 - Amends the Social Security Act (SSA) to add a new title XXI (Healthy Start), incorporating certain current SSA title XI peer review and fraud and abuse provisions. Establishes an entitlement program of health insurance for eligible children under age 13 and mothers-to-be who are not covered under a qualified health plan. Outlines the scope of benefits for such individuals, which generally consist of the same benefits that are available under SSA title XVIII (Medicare) to individuals entitled to benefits under Medicare part A (Hospital Insurance) and enrolled under Medicare part B (Supplementary Medical Insurance), including well child services and pre- and post-natal care provided to such children and women, respectively, without the application of deductibles, coinsurance, or copayments. Entitles to benefits as both a child and a pregnant woman any individual entitled to program benefits as either the one or the other. Creates in the Treasury the Children Health Insurance Trust Fund. Makes necessary appropriations to it out of the premium tax imposed by this Act for use in financing the Healthy Start program.

Amends the Internal Revenue Code to impose: (1) a premium tax on certain individuals covered by the Healthy Start program, with exceptions for certain low-income families, in order to cover uninsured children and mothers-to-be; and (2) certain reporting requirements with regard to qualified health plans (and certain penalties to enforce them).