I don't think anyone every replied to your question about how this works with a family plan..
With all discounts (corporate, student), the way the family plan works is this:
The discount will be applied to the base price of the plan (for example, $59.99 price of the 700 minute calling plan); the additional line(s) will not have a discount applied. The data from the first line would be discounted, but none of the other lines. The bulk of the cost gets discounted, but if you have multiple data plans, you're kinda outta luck. That being said, you can have an iPhone 3G as your "main" (just by title) line that will be discounted, and have an old iPhone (which would not be eligible for discount anyway) as a secondary line.
To answer your question specifically, even though you are the only one who is the student, you can still get the discount on the "whole" account. If multiple people are eligible for discounts, you can only use one (so pick the larger discount).
BTW, the whole process can actually be done online; you never need to talk to anyone to apply the discount to your account.
Note: Most discount plans make upgrade fees ($18/line) free, but you have to call customer service (611 from your phone) to get them taken off retroactively. The good news is that with the corp./student discount, you get to talk to Business Customer Service, which seems to be a LOT better than regular customer service.
My scenario:
$60 700 minutes
$10 extra line
$30 iPhone 3G plan
$12 taxes
-$18 Corp discount
$94 total family plan (2 lines)
Only $4 more than I'm paying now since the new data plan will be eligible for discount ($30 - $20 - 20% x $30)