For i=1,2, let (M_i,D_i) be pairs consisting of a Cartan MASA D_i in a von Neumann algebra M_i, let atom(D_i) be the set of atoms of D_i, and let S_i be the lattice of Bures-closed D_i bimodules in M_i. We show that when M_i have separable preduals, there is a lattice isomorphism between S₁ and S₂ if and only if the sets {(Q₁, Q₂)∈ atom(D_i)× atom(D_i): Q₁M_iQ₂≠ (0)} have the same cardinality. In particular, when D_i is nonatomic, S_i is isomorphic to the lattice of projections in L^∞([0,1],m) where m is Lebesgue measure, regardless of the isomorphism classes of M₁ and M₂.