Building Secure and Healthy Families Act of 2002 - Amends part A (Temporary Assistance for Needy Families) (TANF) of title IV of the Social Security Act to revise the TANF program, with changes: (1) replacing grants for States to reward a decrease in illegitimacy with grants to States to promote and support secure families; (2) adding nondiscrimination requirements pertaining to marital status and family structure and participation in activities or services funded under the new grant; (3) authorizing a State to assist a teenage parent who does not attend high school or another equivalent training program to come into compliance with TANF work and education requirements, and deeming teenage heads of household who maintain satisfactory school attendance to meet work participation requirements; (5) requiring certain certifications regarding domestic or sexual violence in State TANF plans, and prohibiting a State from penalizing an individual for TANF requirement noncompliance where domestic or sexual violence is a significant contributing factor in the noncompliance; (6) deeming a TANF recipient who provides appropriate care to a child or other relative who has a serious health condition or a disability as engaged in work for work participation rate purposes; and (7) eliminating the termination of TANF assistance for an entire family where an individual in the family has refused to engage in required work.