Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an ``imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at non-vanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a {it coherence network} induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.
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