How can I get an iPhone through Apple's iPhone Upgrade Program on my family's Verizon plan?
Yes, virtually any postpaid Verizon customer can sign up for the iPhone Upgrade Program through Apple's web site or in store. (So can Sprint and AT&amp;T customers, although T-Mobile is currently in-store only.)

This is separate from any agreements you have with Verizon, and you will still have to finish paying off your current phone with them.