Can I deduct my Family/Child Healthcare Premiums paid on my weekly pay check through deductions?

Are those premiums pre-tax?  Usually employers deduct premium payments from your paycheck on a pretax basis. Since your employee contributions are already taking advantage of tax savings, you can't deduct them again on your return.

In most cases, the premiums are pre-tax.  You can't subtract (deduct) an item from your taxable income that was already subtracted from your taxable income by your employer. 

In rare cases, your premiums may be partly or wholly after-tax.  This is usual, and should only happen when you providing insurance for someone who is not your child, your spouse or your dependent.  If part of your premiums are after-tax, that can be used as an itemized deduction.