[SumZero]

My quick SWAG:

Part 1:
First consider hand A is suited. There are 13*12/2 such hands.
Part 1a: Consider hand B suited in the same suit. There are 11*10/2 such hands.
Part 1b: Consider hand B suited in some other suit. There are 13*12/2 such hands.
Part 1c: Consider hand B unsuited with 1 card in the hand A suit. There are 11*13 such hands.
Part 1d: Consider hand B unsuited with 0 cards in the hand A suit. There are 13 + 13*12/2 such hands.
Conclusion of part 1: A * B = 78 * 367 = 28,626.

Part 2:
Now consider hand A is a pair. There are 13 such hands.
Part 2a: Consider hand B suited in the same suit as one of the pair cards. There are 12*11/2 such hands.
Part 2b: Consider hand B suited in a different suit than the pair cards. There are 13*12/2 such hands.
Part 2c: Consider hand B unsuited with 1 card in a paired card's suit. There are 12[pairs] + 12*12[unpaired] such hands.
Part 2d: Consider hand B unsuited with both cards in each of the paired card's suit. There are 12[pairs] + 12*11/2[unpaired] such hands.
Part 2e: Consider hand B unsuited with neither card in each of the paired card's suit There are 13[pairs] + 13*12/2[unpaired] such hands.
Conclusion of part 2: A * B = 13 * 469 = 6,097.

Part 3:
Now consider hand A is an unsuited unpaired hand. There are 13*12/2 such hands.
Part 3a: Consider hand B suited in the higher card suit. There are 12*11/2 such hands.
Part 3b: Consider hand B suited in the lower card suit. There are 12*11/2 such hands.
Part 3c: Consider hand B suited in an unused suit. There are 13*12/2 such hands.
Part 3d: Consider hand B paired in the suits of hand A. There are 11 such hands.
Part 3e: Consider hand B paired with 1 card in the suit of the higher card of A and one card in an unused suit. There are 12 such hands.
Part 3f: Consider hand B paired with 1 card in the suit of the lower card of A and one card in an unused suit. There are 12 such hands.
Part 3g: Consider hand B paired in the unused suits. There are 13 such hands.
Part 3h: Consider hand B unpaired unsuited in the two suits of A. There are 11*10/2[no shared ranks]+12[share rank with lower card of A in high card suit]+11[share rank with higher card of A in low card suit but no double count of shared lower card of A in high card suit] such hands.
Part 3i: Consider hand B unpaired and unsuited with one card in same suit as the higher card of A and the other card in an unused suit. There are 12*12 such hands.
Part 3j: Consider hand B unpaired and unsuited with one card in the same suit as the lower card of A and the other card in an unused suit. There are 12*12 such hands.
Part 3k: Consider hand B unpaired unsuited and sharing no suits with A. There are 13*12/2 such hands.
Conclusion of part 3: A * B = 78 * 702 = 54,756.

So I might have miscounted something but that gives me:

28,626 + 6,097 + 54,756 = 89,479 such hands.

But it is late so I may have miscounted.