We have used composition depth profiling of polymer bilayers, based on nuclear reaction analysis, to determine miscibility, phase coexistence, and critical temperatures in mixtures of random olefinic copolymers of mean composition E(1-x)/EE(x); here E is the ethylene group -(C4H,)-, EE is the ethylethylene group -[C2H3(C2H5)]-, and one of the copolymers is partially deuterated. The components in each binary mixture have different values x(1),x(2) of the EE fraction. Using a simple Flory-Huggins mixing model, our results enable us to extract an interaction parameter of the form chi(x(1),x(2),T)=A(x(1),x(2))/T, where for given x(1),x(2), A is a constant. Calculated binodals using this form fit our measured coexistence curves well, while allowing chi a weak composition dependence improves the fit further. Within the range of our parameters, our results suggest that in such binary polyolefin mixtures the interaction parameter increases roughly linearly with the extent of chemical mismatch expressed as the difference in degree of ethyl branching between the two components.