The blood doesn't mix, you're right. But nutrients, O2, CO2, etc. pass through the placenta easily. The fetus gets O2 from the mother because fetal hemoglobin has a higher affinity for O2 that adult hemoglobin does (this is because fetal Hb has a lower affinity for 2,3-BPG). Anyways, the fetal Hb basically "strips" the adult Hb off its O2. This is how the fetus gets oxygen. Hope this helps.