Family Plus Health Care Act of 2022 This bill extends coverage under private health insurance to enrollees' parents who are not eligible for separate coverage under Medicare or Medicaid. Specifically, private health insurers that offer dependent coverage of enrollees' children must also offer coverage of enrollees' parents, at an enrollee's option, if such parents are not eligible for Medicare or Medicaid. The bill also provides for the treatment of such parents as dependents for related tax purposes.