Jet multiplicity distributions in top quark pair (t t ¯) events are measured in pp collisions at a centre-of-mass energy of 8 TeV with the CMS detector at the LHC using a data set corresponding to an integrated luminosity of 19.7fb-1. The measurement is performed in the dilepton decay channels (e +e -, μ+μ-, and e ±μ∓). The absolute and normalized differential cross sections for t t ¯ production are measured as a function of the jet multiplicity in the event for different jet transverse momentum thresholds and the kinematic properties of the leading additional jets. The differential t t ¯ b and t t ¯ b b ¯ cross sections are presented for the first time as a function of the kinematic properties of the leading additional b jets. Furthermore, the fraction of events without additional jets above a threshold is measured as a function of the transverse momenta of the leading additional jets and the scalar sum of the transverse momenta of all additional jets. The data are compared and found to be consistent with predictions from several perturbative quantum chromodynamics event generators and a next-to-leading order calculation.