Student Loan Forgiveness for Frontline Health Workers Act This bill establishes temporary programs to provide federal and private student loan forgiveness to certain frontline health care workers. Frontline health care workers are those individuals who have made significant contributions to the medical response (e.g., patient care, medical research, or testing) to the COVID-19 (i.e., coronavirus disease 2019) national emergency. Specifically, the Department of Education (ED) must carry out a program to forgive the outstanding balance of principal and interest due on federal student loans for borrowers who are frontline health care workers. Additionally, the Department of the Treasury must carry out a program to repay in full the outstanding balance of principal and interest due on certain private student loans for borrowers who are frontline health care workers. ED and Treasury must coordinate to ensure that eligibility determinations are consistent across both programs and that frontline health care workers who are eligible for both programs may apply for loan forgiveness with a single application. Further, such programs must be available to frontline health care workers who were borrowers of eligible loans and who died as a result of COVID-19. The bill specifies the notification requirements related to the availability of these programs. ED, Treasury, and the Department of Health and Human Services must jointly establish an intergovernmental working group to assist with the administration of these programs, including the development of the application process. The bill also excludes discharged student loan debt under these programs from an individual's gross income.