The mixing interactions among polyolefins and other hydrocarbon polymers are of strong fundamental and practical interest, especially in mixtures involving the simplest member of the family, polyethylene (E). The present work examines the interaction energy densities between E and random copolymers of styrene and hydrogenated isoprene (SrhI), and between E and random copolymers of vinylcyclohexane and hydrogenated isoprene (VCHrhI), by measuring the order disorder transition temperatures of near-symmetric E-SrhI and E-VCHrhI diblock-random copolymers The E SrhI case is of special interest, since the solubility parameters delta fall in the order delta(S) > delta(E) > delta(hI); if regular mixing were obeyed, zero interaction energy between E and SrhI could be obtained for a suitable SrhI composition. However, large positive deviations from regular mixing are observed in the E-SrhI system, while smaller but significant negative deviations are observed in the E VCHrhI system. Notwithstanding these irregularities, a ternary mixing model ("copolymer equation"), using independently determined values of the three component interaction energy densities, provides a good representation (within approximate to 15%) of the experimental interaction energies.