We investigate the structure of the D10(2420[2430])(JP=1+) mesons via analyzing the semileptonic Bc→D10lν transition in the frame work of the three-point QCD sum rules and the heavy-quark effective theory. We consider the D10 meson in three ways: as a pure |cu¯⟩ state, as a mixture of the two |3P1⟩ and |1P1⟩ states with a mixing angle θ , and as a combination of the two mentioned states with mixing angle θ=35.3∘ in the heavy-quark limit. Taking into account the gluon condensate contributions, the relevant form factors are obtained for the three above conditions. These form factors are numerically calculated for |cu¯⟩ and the heavy-quark limit cases. The obtained results for the form factors are used to evaluate the decay rates and the branching ratios. Also for mixed states, all of the mentioned physical quantities are plotted with respect to the unknown mixing angle θ .