The structure of a binary mixture of nonadditive hard spheres confined in a slit pore is studied by the integral equations method in which the confining medium acts as a giant particle at infinite dilution. The adsorption/desorption curves are studied as a function of the composition and density, when the homogeneous bulk mixture is near the demixing instability. The Ornstein-Zernike integral equations are solved with the reference functional approximation closure in which the bridge functions are derived from Rosenfeld's hard sphere functional for additive hard sphere. To study the high composition asymmetry regime in which a population inversion occurs, we developed an approximate closure that overcomes the no solution problem of the integral equation. By comparison with simulation data, this method is shown to be sufficiently accurate for predicting the threshold density for the population inversion. The predictions of simpler closure relations are briefly examined.