In my experience the best way to deal with the Immortals is to swamp them with spearmen - Legio Lanciarii seemed to work pretty well, especially if you can get the Clibs to charge into them when they're "braced" - and hit them in the flanks and rear with Household Bodyguards. The HBs have armour-busting maces as secondary weapons too after all, and often seemed to be able to make quite short work of the Immortals. Mind you, Dromedarii (nevermind Armoured Camel Mercs) are surprisingly good as flankers too thanks to their horse-scaring bonuses. Immortals stuck in Lanciarii and enveloped by HBs and Dromedarii usually rout pretty fast and die a dog's death. When I played the ERE I made a point of always having at least two camel units in every field army at the Sassanid front.