I'm not sure of Peter, as he goes from a somewhat typical buffon Dad with a good heart to a very childish and immature person through-out the series (although this character development (yes I'm calling it that) makes him much more funny

). Although he seems to volatile, crazy, and possibility driven much like an Ne dom would be.
Brain, in the first seasons is an INTP 'I'm the aloof observer dude'. But by later seasons I'm more inclined to think that he's actually INFP or ENFP. He clearly demonstrates a lot of Fi (he thinks jailing pot smokers is wrong, think that un-liberal societal values are bad, etc.). But he also seem somewhat extraverted, he clearly dates often and seems to adept well at social locations like clubs or whatnot. Or he could just be an outgoing INFP

Or in fact, whatever Seth MacFarlane's type is since Brian basically is Seth MacFarlane.