Responsible Fatherhood and Healthy Families Act of 2006

Responsible Fatherhood and Healthy Families Act of 2006 - Amends part A (Temporary Assistance for Needy Families) (TANF) of title IV of the Social Security Act (SSA) with respect to: (1) funding for responsible fatherhood programs; (2) requirements to ensure procedures to address domestic violence; (3) activities promoting responsible fatherhood; (4) grants to healthy family partnerships for domestic violence prevention, for services for families and individuals affected by domestic violence, and for developing and implementing best practices; and (5) elimination of separate TANF work participation rate for two-parent families.

Amends SSA title IV part D (Child Support and Establishment of Paternity), as amended by the Deficit Reduction Act of 2005, to prohibit a state from collecting any amount owed to the state by reason of costs it has incurred for the birth of a child for whom support rights have been assigned.

Requires a state to make a full distribution of collected child support to the family.

Directs the Secretary of Health and Human Services to award grants to states for three employment demonstration projects, including: (1) a court- or state child support agency-supervised program for noncustodial parents so they can pay child support obligations; (2) a transitional jobs program combining temporary subsidized employment with skill development activities; and (3) public-private career pathways partnerships.

Conditions continued approval of a state plan under part D upon state assessment of its policies with respect to barriers to employment and financial support of children.

Amends the Food Stamp Act of 1977 with respect to: (1) deductions from family income for child support received in order to qualify for food stamps; (2) verification of child support payments; and (3) inclusion of economic opportunities programs in qualifying work programs.

Amends the Internal Revenue Code to: (1) modify the earned income tax credit; (2) provide an additional tax credit for certain workers required to make child support payments; (3) revise the formula to increase the earned income tax credit for joint returns; (4) revise tax treatment of inverted entities, especially expatriated entities; (5) treat controlled foreign corporations established in tax havens as domestic corporations for tax purposes; and (6) prescribe the taxation of income of controlled foreign corporations attributable to imported property.