Measurements of the jet activity in t (t) over bar events produced in proton-proton collisions at root s = 8 TeV are presented, using 20.3 fb(-1) of data collected by the ATLAS experiment at the Large Hadron Collider. The events were selected in the dilepton e mu decay channel with two identified b-jets. The numbers of additional jets for various jet transverse momentum ( p(T)) thresholds, and the normalised differential cross-sections as a function of p(T) for the five highest-p(T) additional jets, were measured in the jet pseudorapidity range broken vertical bar eta broken vertical bar < 4.5. The gap fraction, the fraction of events which do not contain an additional jet in a central rapidity region, was measured for several rapidity intervals as a function of the minimum p(T) of a single jet or the scalar sum of p(T) of all additional jets. These fractions were also measured in different intervals of the invariant mass of the e mu b<(b)over bar> b system. All measurements were corrected for detector effects, and found to be mostly well-described by predictions from next-to-leading-order and leading-order t (t) over bar t event generators with appropriate parameter choices. The results can be used to further optimise the parameters used in such generators.