The characteristics of the interface between immiscible polymers, semicrystalline polyethylene (PE) and amorphous deuterated polystyrene (dPS), were determined in the melt state, using the neutron reflectivity technique. The neutron reflectivity profiles of PE-dPS bilayer samples were measured in situ at 150 degrees C in the melt regime giving a melt interfacial roughness, sigma(12), of 1.18 +/- 0.33 nm. The measured interfacial width consists of a true interfacial width, l(t), convoluted with a width, l(0). The latter has been variously described by a number of authors as a capillary wave interfacial width or an initial width. From the true interfacial width the Flory-Huggins-Stavermann interaction parameter, chi, was calculated. The calculated values of chi were shown to differ by almost an order of magnitude from each other depending on the definition of l(0) used. These values are compared with other values of chi obtained via theoretical interpretations of interfacial tension measurements and solubility parameter determination. It is shown that neither definition of l(0) is totally satisfactory.