Dual Coverage

Would a child on their parent's plan be removed if they become eligible through their current employer's health insurance plan? More specifically, could said child only sign up for their new employer's dental and vision plan but opt out of the employer's medical plan while staying on their parent's BCBSOK Medical/Dental/Vision plan? I know that I can stay on my parent's plan due to the health insurance reform act, but am I allowed to double dip just on dental & vision?