Well, if I'm paying into the NHS (which I would be) would I and my family(spouse and soon to be 16 year old) not be entitled to the services?
You will be entitled to 'free' NHS healthcare, as you will each be paying the IHS surcharge to cover you for NHS healthcare (and you will be paying taxes towards it as well).
The IHS surcharge is currently £200 per year of the visa (£600 each paid at time of application), but it will be doubling to £400 per year (£1,200 each) sometime this year. It used to be that Tier 2 ICT visa holders did not have to pay the IHS surcharge, but this changed last year.
The private healthcare offered by the company will be an added extra on top of NHS healthcare, and because you will generally use the NHS in the first instance, UK private healthcare/insurance is really only used as a top up. Quite a few companies do offer health insurance as a benefit of employment, but even if you don't have any insurance, you'll still be able to get NHS healthcare.
For example:
- if you get an NHS referral to a specialist, you could use the insurance to see a private specialist
- to skip the waiting lines for surgeries/procedures
- to cover elective surgeries that aren't available on the NHS (like cosmetic surgery),
- to cover medications that may be too expensive or too new/experimental to be offered on the NHS (which isn't many, really).