An independent contractor is considered "self-employed" by the IRS, and therefore files Schedule C as part of the tax return.
Generally, having dependents will not alter this (perhaps I misunderstood the thrust of your question as it was cut off); you will enter the dependents as normal in Personal Info.
However, note that how you treat health insurance premiums for you and your family is a little different than what you might expect. Please see this answer from Coleen which describes how to enter these premiums.
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