The blend miscibilities of deuterated polystyrene (dPS) and sulfonated poly(styrene-ran-styrenesulfonate) (P(S-SS)) are examined by using forward recoil spectrometry (FRES) to probe the intermixing of bilayer films. This method directly determined the equilibrium coexistence compositions for dPS:P(S-SSx) blends where the degree of sulfonation (x) ranged from 0.2 to 2.6 mol %. In the temperature range 150-190 degrees C, FRES profiles reveal full miscibility for x <= 0.2 mol % and complete immiscibility for x >= 2.6 mol %. Partial miscibility exists in dPS:P(S-SSx) blends with x = 0.7, 4.0, and 1.2 mol %, where between 150 and 190 degrees C the coexisting compositions show upper critical solution temperature (UCST) phase behavior. Blend interaction parameters, chi(blend), are calculated using the Flory-Huggins theory and the coexisting compositions of the partially miscible bilayers. The copolymer blend theory estimates the styrene-styrenesulfonate segmental interaction parameter to be extraordinarily large, chi(S/SS) >= 25. While the applicability of mean-field approaches is limited in this profoundly incompatible system, recent theories about random copolymers have established criteria for "self-demixing" due to their inherent compositional variations. Our estimate of the monomer-monomer interaction parameter suggests the potential for demixing in P(S-SSx) random copolymers that possess even a narrow distribution of compositions.