On AT&T, can you trade/switch plans with another line on Family Talk?

My dad has been grandfathered in with unlimited data, and sadly when I received my first iPhone back in 2011, unlimited data did not exist anymore. It's now 2013 and I have an iPhone 5, with 2GB, and this plan isn't working for me since I've been receiving those dreadful text messages every month and since my dad uses less than 2GB a month, we were wondering if we can trade/switch our data plans, so I'll have unlimited and he'll have 2GB. Is it possible to do that?