Adding your parents to your employee health insurance plan may be an option, depending on your employer and the insurance carrier. Some employers offer coverage to employees' eligible family members, while others do not. And some insurance carriers will only offer coverage to employees, while others will also offer coverage to eligible family members.
If your employer offers coverage to employees' eligible family members, and your insurance carrier offers coverage to family members, then you should be able to add your parents to your employee health insurance plan. You will likely need to provide proof of your parents' relationship to you (e.g., a birth certificate or marriage certificate), as well as proof of their eligibility for coverage (e.g., a Social Security number or green card).
If your employer does not offer coverage to employees' eligible family members, or if your insurance carrier does not offer coverage to family members, then you will not be able to add your parents to your employee health insurance plan. In this case, you may want to consider other health insurance options for your parents, such as a private health insurance plan or a health insurance marketplace plan.