We present a study of the decays B0→D0K*0 and B0→D̄0K*0 with K*0→K+π-. The D0 and the D̄0 mesons are reconstructed in the final states f=K+π-, K+π-π0, K+π-π+π-, and their charge conjugates. Using a sample of 465×106 BB̄ pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC, we measure the ratio RADS[Γ(B̄0→[f] DK̄*0)+Γ(B0→[f̄]DK*0)]/[Γ(B̄0→ [f̄]DK̄*0)+Γ(B0→[f]DK*0)] for the three final states. We do not find significant evidence for a signal and set the following limits at 95% probability: RADS(Kπ)<0.244, RADS(Kππ0)<0.181, and RADS(Kπππ)<0.391. From the combination of these three results, we find that the ratio rS between the b→u and the b→c amplitudes lies in the range [0.07,0.41] at 95% probability. © 2009 The American Physical Society.