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) BB ¯ 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[over ¯]→D^{(*)}π^{+}π^{-}ℓ^{-}ν[over ¯])/B(B[over ¯]→D^{(*)}ℓ^{-}ν[over ¯]) 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[over ¯]→D^{(*)}ππℓ^{-}ν[over ¯] 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.