Refinance through the same bank?

Is it possible to refinance through the bank that holds your mortgage? Is it desirable? Is it easier? I bought a house in August with a Bank of America no fee mortgage at 7%. I'm wondering if a) it makes sense to refinance now, even just a few months in, and b), whether I should approach the mortgage holder first and see what they can do. It seems to make sense that they'd want to keep the business rather than letting it go to another company, but I'm wondering if I'm missing something, since the web seems to have little info on doing so. Other salient facts: 30 year, fixed rate, 10% down. I'd be willing to consider a 15 year mortgage if the rate is low enough now, because we could probably afford it. We plan on staying here for at least 5 to 10 years, possibly longer.