We provide a general theorem implying that for a (strongly) dependent theory T the theory of sufficiently well-behaved pairs of models of T is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank one theories as well as to a setting of dense pairs of first-order topological theories.
Alexander Berenstein. Alf Dolich. Alf Onshuus. "The independence property in generalized dense pairs of structures." J. Symbolic Logic 76 (2) 391 - 404, June 2011. https://doi.org/10.2178/jsl/1305810754