Is it ethical to leave an unpaid internship at a newspaper to freelance for another outlet?

I know this story might be better suited for Randy Cohen of The Ethicist, but here’s my question:

I'm an undergraduate student. Last summer, I worked as a paid intern for a daily newspaper. I am receiving academic credit this summer. The editors usually assign me one or two stories a week in addition to office work. Lately, they've been asking me to write some stories on nights and weekends, but not much during business hours. I realize that they are probably being nice and that the clips that I am getting might help me in my career. However, I am not keen on covering an event for free on weekends when paid staff reporters or even freelancers might otherwise work.

There's a competing start-up website in a nearby community that seems to be using a lot of freelancers. If I were to approach them and they were willing to take me on, is it ethical to leave my unpaid summer internship? I’m not the only intern in the office and the paper would not be left short-handed.

I should mention that I have a bias. My college paper graciously pays me a nominal amount of money for my work. I do realize that clips from a college paper versus an established daily are of two different qualities. And don’t get me wrong: I am grateful towards the paper for the internship.