Because the big beams sat directly on top of the posts holding the deck up, we couldn't just continue the main posts up through the deck. The alternative is to bolt 4x4 posts onto the outside of the deck, which we did.
Our beams are so thick that we ended up using 8" x 1/2" machine bolts to hold the posts on. While they don't overlap the beams as much as I would like, they seem really solid. The offset bolts grab more of the overlapping surface area, and let you adjust the alignment of the posts a bit by cranking one down tighter than the other.