Dihadron correlations at high transverse momentum p(T) in d+Au collisions at root s(NN)=200 GeV at midrapidity are measured by the PHENIX experiment at the Relativistic Heavy Ion Collider. From these correlations, we extract several structural characteristics of jets: the root-mean-squared transverse momentum of fragmenting hadrons with respect to the jet root < j(T)(2)>, the mean sine-squared of the azimuthal angle between the jet axes < sin(2)phi(jj)>, and the number of particles produced within the dijet that are associated with a high-p(T) particle (dN/dx(E) distributions). We observe that the fragmentation characteristics of jets in d+Au collisions are very similar to those in p+p collisions and that there is little dependence on the centrality of the d+Au collision. This is consistent with the nuclear medium having little influence on the fragmentation process. Furthermore, there is no statistically significant increase in the value of < sin(2)phi(jj)> from p+p to d+Au collisions. This constrains the effect of multiple scattering that partons undergo in the cold nuclear medium before and after a hard collision.