We present branching fraction measurements for the decays B0→ρ0K *0, B0→f 0K *0, and B0→ρ -K *+, where K * is an S-wave (Kπ)0* or a K *(892) meson; we also measure B0→f 0K2*(1430)0. For the K *(892) channels, we report measurements of longitudinal polarization fractions (for ρ final states) and direct CP violation asymmetries. These results are obtained from a sample of (471.0±2.8) ×106 BB̄ pairs collected with the BABAR detector at the PEP-II asymmetric-energy e +e - collider at the SLAC National Accelerator Laboratory. We observe ρ0K *(892)0, ρ0(Kπ)0*0, f 0K *(892)0, and ρ -K *(892) + with greater than 5σ significance, including systematics. We report first evidence for f 0(Kπ)0*0 and f 0K2*(1430)0, and place an upper limit on ρ -(Kπ)0*+. Our results in the K *(892) channels are consistent with no direct CP violation. © 2012 American Physical Society.