Branching fraction measurements of charmless B0→K*0h1+h2- (h1,2=K, π) decays are presented, using a data sample of 383×106 Υ(4S)→BB̄ decays collected with the BABAR detector at the PEP-II asymmetric-energy B-meson factory at SLAC. The results are B(B0→K* 0K+K-)=(27.5±1.3±2.2)×10-6, B(B0→K*0π+K-)=(4. 6±1.1±0.8)×10-6, and B(B0→K*0π+π-)=(54. 5±2.9±4.3)×10-6. The first errors quoted are statistical and the second are systematic. An upper limit is set for B(B0→K*0K+π- )<2.2×10-6 at 90% confidence level. We also present measurements of CP-violating asymmetries for the observed decays. © 2007 The American Physical Society.