If you're younger than 26, you can remain on your parents' health insurance even if your employer offers a health plan of its own. It doesn't matter if you're married, living apart from your parents, financially independent or attending school.
When Coverage Ends
Insurance plans that offer dependent coverage are required to offer coverage to dependents until they turn 26. The day you turn that age, you lose coverage. However, the loss of health insurance coverage qualifies as a life event, meaning you'll have 30 days to enroll in your employer's health care plan even if it's not open enrollment season. You also qualify for a Special Enrollment Period to purchase insurance through the Health Insurance Marketplace. As of March 2015, that window is 60 days. If you don't enroll in that time, however, you may be out of luck until the next Open Enrollment Period.