My wife was reading up on religious studies and her books mentioned that in 1230 Portugal and Aragon was a part of The Holy Roman Empire.
This sounded rather odd to me, and I haven't been able to find any other sources that confirm it. Do anyone here know if this was the case?
No, in 1230 Aragon was an independent kingdom; I have no idea where anyone would get that idea. I don't know much about Portugal, but I highly doubt it. In the Middle Ages kings or emperors could make all sorts of claims, but they didn't necessarily equate to actual rule. So, while it's not far-fetched that maybe Frederick II (Holy Roman Emperor in 1230) made some sort of claim on Spain (I think one of his daughters married Peter III of Aragon in the 1270's), any such claim couldn't have any legitimacy.
In the early modern era the Kingdom of Spain (and hence Aragon) was ruled by a cadet branch of the Hapsburg family, who also technically ruled the "Holy Roman Empire"; but the Holy Roman Empire was a thing, and the Kingdom of Spain was a different thing. Some historians have spoken of a "Hapsburg Empire" in this sense.
Could it be that the book meant to show the Ghibellines?
Because the only thing I can find which could link Aragon, Portugal and the HRE around 1230 is their common enemy in Innocent IV.
Innocent IV. excommunicated Emperor Frederick II. multiple times, he gave grounds for the deposition of Sancho II. of Portugal, and he helped the French to aquire Toulouse, which was a part of Aragon before 1229. Also, there was a lot of bad blood between Innocent and at least Frederick and Aragon caused by Italian affaires.