Refraction: given an incoming and transmitted direction, can I deduce the normal?
See equation (16) in Microfacet Models for Refraction through Rough Surfaces : $-(\eta_i w_i + \eta_o w_o)$ which you'll probably want to normalize. $\eta$ are the two indices of refraction and $w$ the two vectors (they use $i$ and $o$ in the paper). Also look at the left part of figure 7 on the same page to see where all the vectors are pointing.