Family and Retirement Health Investment Act of 2013 - Amends the Internal Revenue Code, with respect to health savings accounts (HSAs), to allow:

• spouses who have both attained age 55 to make increased catch-up contributions to the same HSA;
• Medicare Part A (hospital insurance benefits) beneficiaries to participate in an HSA;
• Medicare beneficiaries participating in an Archer medical savings account designated as a Medicare Advantage MSA to contribute to an HSA;
• veterans eligible for service-connected disability benefits and individuals eligible for Indian health service assistance to participate in an HSA;
• individuals eligible to receive benefits under certain TRICARE plans to participate in an HSA;
• participants in flexible spending arrangement or a health reimbursement arrangement to contribute to an HSA;
• payments from an HSA for prescription and over-the-counter medicine or drugs;
• the use of HSAs to purchase certain health insurance coverage and long-term care insurance;
• payment of certain medical expenses from an HSA incurred before the establishment of an HSA; and
• individuals who receive primary care services for a fixed periodic fee to participate in an HSA.

Amends the bankruptcy code to treat HSAs as tax-exempt individual retirement accounts (IRAs) for purposes of exempting them from creditor claims.

Reauthorizes the use of Medicaid health opportunity accounts.

Treats membership in a tax-exempt health care sharing ministry as coverage under a high deductible health plan for purposes of the tax deduction for contributions to an HSA.

Amends the Patient Protection and Affordable Care Act (PPACA) to treat a high deductible health plan in which an enrollee has established an HSA as a qualified health plan.

Amends the Public Health Service Act to exempt from lifetime limits on the dollar value of benefits for any participant in or beneficiary of a group health plan any health reimbursement arrangement which permits the purchase of a qualified health plan through a state health insurance exchange established under PPACA.

Treats as medical care for purposes of the tax deduction for medical expenses certain exercise equipment and physical fitness programs, nutritional and dietary supplements, and periodic fees paid to a primary physician, physician assistant, or nurse practitioner.

Repeals provisions of PPACA that impose annual limitations on deductibles for health plans offered in the small group market.