I believe there are a lot of charts online that talk about what is and isn't possible with blood groups. My knowledge of this is incomplete, and a lot of the charts also say things like "in rare circumstances," and go on to give exceptions that are a little hard to understand.
That said, it doesn't sound like it is unusual for the child to have different blood group from the parents if the parents themselves have different blood groups from each other. But (again, please check this with someone more knowledgeable) it appears the child would have to get one letter from one parent and one from the other.
What I would do in the case you have described is to reconfirm the assertion that the parents are both type B and the child is type AB. If a question of paternity is riding on it, it would not be too cautious for both parents to get their blood type checked with new tests. Then have the child's blood tested (again) as well. This is to prevent jumping to conclusions. A lot of grief could be prevented if the couple were to find out their blood types weren't what they thought.
For example, my husband's blood type is A, why does he know this? Because he thinks it was on his Army dogtag 30 years ago. Mine is O. Why do I know this? Because I think my doctor told it to me once. If I had a paternity question I was trying to solve using blood types, I would certainly not rely on such poor evidence. I'd test again, and test him again and then talk to an expert, before I would use blood tests as the basis of accusations.
I might also add, DNA tests might be cheaper than blood tests, if the question is a paternity question.