We report on measurements of the decays of B mesons into the semileptonic final states B arrow right D(*)pi+ pi- scriptl- nu, where D(*) represents a D or D* meson and scriptl- is an electron or a muon. These measurements are based on 471x10 super(6) BB pairs recorded with the BABAR detector at the SLAC asymmetric B factory PEP-II. We determine the branching fraction ratios R(*) sub(pi+ pi- ) = scriptB(B arrow right D(*)pi+ pi- scriptl- nu) using events in which the second B meson is fully reconstructed. We find R(*) sub(pi+ pi-) = 0.067+ or -0.010+ or -0.008 and R* sub(pi+pi-)=0.019+ or -0.005+ or -0.004, where the first uncertainty is statistical and the second is systematic. Based on these results and assuming isospin invariance, we estimate that B arrow right D(*)pipiscriptl-nu decays, where pi denotes either a pi + or - and pi sub(0) meson, account for up to half the difference between the measured inclusive semileptonic branching fraction to charm hadrons and the corresponding sum of previously measured exclusive branching fractions.