Let's start off with the ABO blood group first. The child could be of group A, B, O or AB, depending on the alleles present in you and your wife's gene.
Since your wife is group B, she will have antibodies against the A antigens [i.e. her blood group is incompatible with group AB and group A]. Those antibodies can cross over to the placenta and 'attack' the foetus's red blood cells if the foetus blood group is A or AB.

As for the rhesus group, this will not cause any harm to the baby if this is ur FIRST child. Usually during the first pregnancy, if baby is Rhesus positive and mum is Rhesus negative, the doctor will administer 'Rhogam' to the mum within 72 hours of post delivery. This is because during delivery, some of the baby's blood can leak into the maternal body circulation, and thus will stimulate the production of Rhesus antigen antibodies. And if the second pregnancy resulted in a rhesus positive foetus, the antibodies will cross over placenta and attack the foetal red blood cells, causing haemolytic disease of newborn.Therefore the Rhogam is to neutralise the Rhesus antibodies.

Not to worry too much, you can always go for antenatal screening at your local clinic, and the doctor will explain in much clearer details to you. =]hope this helps.

In theory, if both parents are of blood group O positive, the only possible blood group for the offspring is group O positive.

Surely, yes. Rh incompatibility may arise only if mother is Rh-ve and father is Rh ve

No problem!Go Ahead!