Measurements of inclusive and normalized differential cross sections of the associated production of top quark-antiquark and bottom quark-antiquark pairs, t (t) over barb (b) over bar, are presented. The results are based on data from proton-proton collisions collected by the CMS detector at a centre-of-mass energy of 13TeV, corresponding to an integrated luminosity of 138 fb(-1). The cross sections are measured in the lepton+jets decay channel of the top quark pair, using events containing exactly one isolated electron or muon and at least five jets. Measurements are made in four fiducial phase space regions, targeting different aspects of the t (t) over barb (b) over bar process. Distributions are unfolded to the particle level through maximum likelihood fits, and compared with predictions from several event generators. The inclusive cross section measurements of this process in the fiducial phase space regions are the most precise to date. In most cases, the measured inclusive cross sections exceed the predictions with the chosen generator settings. The only exception is when using a particular choice of dynamic renormalization scale, mu(R) = 1/2 Pi(i=t), (t) over bar ,b (b) over bar m(T, i)(,)(1/4) where m(T), (2)(i) = m(i)(2) + p(T,i)(2) are the transverse masses of top and bottom quarks. The differential cross sections show varying degrees of compatibility with the theoretical predictions, and none of the tested generators with the chosen settings simultaneously describe all the measured distributions.