We report on measurements of the decays of ¯ B mesons into the semileptonic final states ¯ B → D ( * ) π + π − ℓ − ¯ ν , where D ( * ) represents a D or D ∗ meson and ℓ − is an electron or a muon. These measurements are based on 471 × 10 6 B ¯ B pairs recorded with the BABAR detector at the SLAC asymmetric B factory PEP-II. We determine the branching fraction ratios R ( * ) π + π − = B ( ¯ B → D ( * ) π + π − ℓ − ¯ ν ) / B ( ¯ B → D ( * ) ℓ − ¯ ν ) using events in which the second B meson is fully reconstructed. We find R π + π − = 0.067 ± 0.010 ± 0.008 and R ∗ π + π − = 0.019 ± 0.005 ± 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 → D ( * ) π π ℓ − ¯ ν decays, where π denotes either a π ± and π 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.