You can deduct what you pay for your own and your family's health insurance regardless of whether it is subsidized by your employer or not, as well
as all other medical and
dental expenses for your family, as an itemized deduction
on Schedule A of Form 1040, but only to the extent that the
total exceeds 7.5% of your Adjusted Gross Income (AGI)
(10% on tax returns for year 2013 onwards).
As pointed out in KeithB's comment, you cannot deduct
any health insurance premium (or other medical expense)
that was paid for out of pre-tax dollars, nor indeed
can you deduct any medical expense to the extent that
it was paid for by the insurance company directly to
hospital or doctor (or reimbursed to you) for
a covered expense; e.g. if the insurance company reimbursed
you $72 for a claim for a doctor's visit for which you
paid $100 to the doctor, only $28 goes on Schedule A
to be added to the amount that you will be comparing
to the 7.5% of AGI threshold, and the $72 is not
income to you that needs to be reported on Form 1040.
Depending on other items on Schedule A, your total itemized
deductions might not exceed the standard deduction, in which
case you will likely choose to use the standard deduction.
In this case, you "lose" the deduction for medical expenses
as well as all other expenses deductible on Schedule A.
Summary of some of the discussions in the comments
Health care insurance premiums cannot be paid for
from HSA accounts (IRS Pub 969, page 8, column 2, near
the bottom) though there are some exceptions. Nor
can health care insurance premiums be paid from an
FSA account (IRS Pub 969, page 17, column 1, near the top).
If you have a business on the side and file a Schedule C
as a self-employed person, you can buy medical insurance
for that business's employees (and their families
too, if you like) as an employment benefit, and pay for it out of
the income of the Schedule C business, (thus saving on taxes).
But be aware that if you have employees
other than yourself in the side business, they would need
to be covered by the same policy too. You can even
decide to pay all medical expenses of your
employees and their
families too (no 7.5% limitation there!) as an employment
benefit but again, you
cannot discriminate against other employees (if any)
of the Schedule C business in this matter. Of course,
all this money that reduced your Schedule C income
does not go on Schedule A at all.
If your employer permits your family to be covered under
its health insurance plan (for a cost, of course), check
whether you are allowed to pay for the insurance with
pre-tax dollars. The private (non-Schedule C)
insurance would, of course,
be paid for with post-tax dollars. I would doubt that
you would be able to save enough money on taxes to make
up the difference between $1330/month and $600/month, but
it might also be that the private insurance policy covers
a lot less than your employer's policy does. As a rule of
thumb, group insurance through an employer can be expected
to offer better coverage than privately purchased insurance.
Whether the added coverage is worth the additional cost is a
different matter. But while considering this matter,
keep in mind that privately purchased insurance is not
to be renewable, and a company might decline to renew a
policy if there were a large number of claims. A replacement
policy might not cover pre-existing conditions for some
time (six months? a year?) or maybe even permanently. So,
do consider these aspects as well. Of course, an employer
can also change health insurance plans or drop them
entirely as an employment benefit (or you might quit
and go work for a different company), but as long as
the employer's health plan is in
existence, you (and continuing members of your
family) cannot be discriminated against and denied
coverage under the employer's plan.