The HAMP program does not generally reduce principal, it will change your rate and terms (length of the loan). The DOJ program could reduce principle. You should contact BOA and the can evaluate your situation.
Many lenders do not give you the option chose. They often limit their modification options to one or the other OR they might require you to first consider one before the other is offered. In the end, you must decide whether whatever is offered is acceptable. What you say you want is the best of all possibilities - principal reduction today AND a lower interest rate. It might be possible BUT if not AND you really want to keep your home - be flexible. If BOA offers you an affordable payment, they may not forgive principal, but they may forbear amortization meaning that when the modified loan eventually matures, you will have a balloon to pay for whatever principal remains. Many borrowers don't like this BUT that's the situation you are in today if you don't modify - you otherwise face a foreclosure or the option of paying a substantially larger balloon payment today just to keep your home.
DOJ Nation Settlement is a Modification offered through U.S. Department of Justice and State Attorneys General global settlement with major mortgage servicers, including Bank of America, N.A. This modification could offer you significant principal reduction and low payments but you would have to be eligible as not everybody is. The program has specific guidelines that you should review.
HAMP is a Modification offered through Making Homes Affordable and does not offer Principle Reduction or guarantee lower payments with their Modifications or at least not as good as the DOJ Nation Settlement.