What I meant (contra jsfisher) is that it is false that two disjoint sets can have "nothing" in common. What I was trying to illustrate with my little poem is that roses and violets are disjoint sets (in, say, the universe of plant species), yet they have a common property: they have leaves.
Somewhat more formally, even though a set A (eg, roses) and a set B (eg, violets) are disjoint, there can be a third set C (eg, plants with leaves) that intersects them both, in which case at least some elements of A and some elements of B would have in common the property represented by C.
What A and B cannot have, if they are disjoint sets, is any common element. If x is an element of A, then x cannot be an element of B. Nonetheless, A and B can have properties (e.g., leaves) in common.
The central question. then, is whether the thing that Jabba claims that H and ~H have in common is a property or an element. I have no idea what this thing he claims they have in common is, although I have tried to go back and figure it out. Having been gone for a week, it's remarkable how, in one sense, I've missed so much; yet in another, so little.