The thermal stability of Langmuir-Blodgett multilayers of cadmium arachidate and perdeuterated cadmium arachidate layers deposited on hydrophobic silicon is investigated by neutron and X-ray reflectometry. Using this pair of techniques allows one to depth resolve changes induced by annealing and also to discriminate between the behavior of the Cd head lattice and that of the aliphatic tails. All samples initially have ill-defined interfaces between the tails of adjoining protonated and deuterated layers, and some interchange of chains among layers occurs during the deposition process itself. The form of the multilayer structure is thermally stable at 70 and 84 degrees C, even though aliphatic tails are lost gradually due to ablation, leading to noticeable losses when annealing for 1 week at 84 degrees C, These losses occur almost exclusively from the layers closest to air, suggesting that the rate of ablation is considerably higher than that of interdiffusion. There appears to be little interlayer interdiffusion of chains when annealing for several hours at 84 degrees C. We conjecture that the type of interaction anchoring the two layers adjoining an interface may influence the stability of that interface to molecular exchange across it.