The microscopic polymer reference interaction site model theory is applied to study the structural correlations of dilute spherical nanoparticles dissolved in AB copolymer melts of variable architecture (alternating, random), composition, and monomer-nanoparticle adsorption strengths that span the depletion, steric stabilization, and bridging regimes. Comparison of the calculations of the monomer-particle pair correlations and polymer-mediated nanoparticle potential of mean force (PMF) with the behavior of reference homopolymers and a binary AB blend are also performed. All intermonomer potentials are hard core, which precludes polymer macrophase or microphase separation, thereby allowing the consequences of differential monomer wettability on nanoparticle spatial organization to be isolated. For each copolymer case, one monomer species adsorbs more strongly on the filler than the other, mimicking a specific attraction. The PMF for the alternating copolymer is similar to that of an analogous homopolymer with additional spatial modulation or layering features. Random copolymers, and the polymer blend, mediate a novel strong and spatially long-range attractive bridging type interaction between nanoparticles at moderate to high adsorption strengths. The depth of this attraction in the PMF is a nonmonotonic function of random copolymer composition, reflecting subtle competing enthalpic and entropic considerations. Virial-based estimates of the maximum solubility of nanoparticles are computed.