You have pairs of chromosomes so your mother has an "A" on one and a "B" on the other. She donates one of these to you.
Your Dad has a "B" on each chromosome and donates one of these.
This means that you'd either be AB or B
(which is actually BB)
Mother's blood being AB and father's blood being B.. that would mean ... *flips abascus*... the kids can end up being of AB blood, B blood and A blood. No possibility of O, unless you involve foul play (sic).
If partner 1#'s blood is of A group and partner 2#'s blood is of B, there is a possibility of getting all four blood groups. I bet that caused a lot of riots in households when they haven't figured out the blood groups