What are all of the possible genotypes if a woman with type A blood and a man with type B blood have children?

The trait of blood type in humans has three alleles—A, B, and O. The alleles for A and B are co-dominant and the allele for type O is recessive.

If both parents mentioned in the question are heterozygotes, their genetic makeup would be AO and BO—with each carrying a recessive O allele.

In a cross, the offspring produced are 25% type AB, 25% type B, 25% type A, and 25% type O.

Therefore, these parents have a 1/4 chance of producing any of the four blood types every time they produce a child. 

I have included a link showing a Punnett square with these two parental genotypes and the outcomes.