It's a shame that there are no books on Ancient Iran in the reading list. Nonetheless, I can recommend some general books on the Achaemenid Empire. First, I recommend Amelie Kuhrt's The Persian Empire, which is a compilation of ancient sources on the Persian Empire in English translation. While it is not a narrative history, it provides all of the primary sources from which we write our modern histories of the Persian. Second, I highly recommend Pierre Briant's From Cyrus to Alexander, a comprehensive history of the Persian Empire. The book is somewhat dense, but it provides an excellent perspective of a modern historian's approaches to an empire that provides numerous historiographical issues.

Unfortunately, I am less knowledgeable about the Parthians, but I know that Daniel Potts' The Archaeology of Elam contains a valuable chapter on post-Achaemenid Iran that includes both textual and archaeological material in its analysis of that region in the period.