Understanding the interfacial organization of heteropolymers near solid surfaces is an issue of fundamental interest that is relevant for many technological and biological applications. In this paper we address several questions pertaining to the surface-induced ordering and the adsorption-desorption phase behavior of a dilute solution of two-letter random heteropolymers interacting with a solid surface. Our analysis is based on a statistical field theoretic formulation of the propagator for the problem of interest. We employ the replica trick to alleviate analytical difficulties which arise when considering averaging over the sequence distribution of the A and the B units. In order to highlight the effects of the surface, we consider the situation wherein the intersegment interactions are of the excluded volume type while the segment-surface interactions of the A and B segments are arbitrarily different. Within the replica symmetric solution, we show that proper coarse-graining of the interaction potentials leads to exact analytical expressions for the self-consistent propagator of the heteropolymer at theta conditions and for the case where excluded volume interactions prevail. One of our interesting findings is that heteropolymers undergo an adsorption-desorption transition in the vicinity of a surface that interacts with the different types of segments in arbitrarily different ways. This is consistent with our previous numerical findings for much more restricted circumstances. We explicitly analyze the influence of the fluctuations in the sequence distribution on the conformational organization of the adsorbed chains and obtain the scaling behavior of properties of interest in the vicinity of the adsorption-desorption threshold with respect to the disorder strength and other polymer interaction parameters. Specifically, invoking the Ehrenfest theorem we find that the adsorption-desorption transition at theta conditions is a second-order phase transition while in the case where excluded volume interaction prevails the transition becomes first order. We also obtain exact analytical expressions for the adsorption-desorption threshold. The threshold exhibits quite an unusual dependence on the strength of the disorder. Finally, we compute the point of onset of repulsive forces between plates that confine a random copolymer solution as a function of chain sequence distribution. We suggest specific experiments employing the surface force apparatus that could directly test our predictions.