Yes*. Just because you are eligible for coverage through your employer does not mean you cannot stay on your parent’s health insurance plan — that is, of course, if you are age 26 or younger.
If your parent’s plan seems like a better fit for your family’s budget, lifestyle, or health care needs, staying on your parent’s plan may be the best option for you!
*Note, the only exception would be if your parent’s plan is a grandfathered plan (meaning it has been in effect prior to March 23, 2010 without any significant changes since then). Until 2014, grandfathered group plans did not have to offer dependent coverage up to age 26 if a young adult is eligible for group coverage outside their parent’s plan. But once a grandfathered plan passes its renewal date in 2014, it must offer coverage through age 26 (assuming the plan offers dependent coverage).