  We estimate the strength of interaction-enhanced coherence between two
graphene or topological insulator surface-state layers by solving
imaginary-axis gap equations in the random phase approximation. Using a
self-consistent treatment of dynamic screening of Coulomb interactions in the
gapped phase, we show that the excitonic gap can reach values on the order of
the Fermi energy at strong interactions. The gap is discontinuous as a function
of interlayer separation and effective fine structure constant, revealing a
first order phase transition between effectively incoherent and interlayer
coherent phases. To achieve the regime of strong coherence the interlayer
separation must be smaller than the Fermi wavelength, and the extrinsic
screening of the medium embedding the Dirac layers must be negligible. In the
case of a graphene double-layer we comment on the supportive role of the remote
$\pi$-bands neglected in the two-band Dirac model.
