We present rigorous calculations for the long-range intensity correlations in multiple wave scattering from a disorder medium. General relations are derived beyond the Born approximation for both the scattering amplitude and the Hikami vertex. The correlations between reflection and transmission coefficients are analyzed for a thick slab within the framework of the diffusion approximation. Besides the coherent contribution to the correlation function, the incoherent one is considered in detail. Conditions are discussed under which the incoherent contribution becomes particularly prominent.