A household employer is not required to pay for his/her employee's health premiums. The direct payment or reimbursement of premiums by the employer is only tax-free to the nanny and the employer if the employer only has one employee. If the employer has 2 or more household employees (like a nanny and a housekeeper) it is no longer tax-free.

I showed my bosses how much mine was every month and they wrote me a separate check on the first payday of the month to cover it.

You it the premiums, she pays the usage/copayments/deductible.