Prove language is NP-Complete

How can I show that the following language is NP-Complete?

{(G, H) : G is a graph and H is a set of induced subgraphs of G such that it is possible to split the vertices of G into two sets A and B so that every subgraph in H contains at least one vertex from A and at least one vertex from B}

I have already proved that the language is in NP, so now it remains to show there is some polynomial time reduction from an NP-Complete language to this one.

Ideally, the solution would use either SAT or 3SAT as the starting point, since these are the languages I've seen being used for previous reductions.

I'm stuck at this point.

As a side note, the phrasing of this problem is a little bit suspect, as the edges of the graphs are not used in the problem statement. (In particular, whether or not $(G,H)\in L$ is independent of the edges in $G$.) Unless I'm missing something, $G$ might as well be a set (with subsets in $H$) instead of a graph.