Interject means to insert between other elements; interpose.
An interjection, therefore, is a word, phrase, or sound said as an aside to express emotions such as: disgust, joy, surprise, etc. Interjections have an independent position. They can be interjected at the beginning, middle or end of a sentence. Hence the meaning of its Latin root.
An interjection is a word solely designed to convey emotion. It expresses meaning or feeling. It does not relate grammatically to the other parts of the sentence, or help the reader understand the relationship between words and phrases in the sentence. Instead, it simply conveys to the reader the way the author is feeling.
A parenthetical element is a word or group of words that interrupts the flow of a sentence and adds additional (but nonessential) information to that sentence.
By this definition, when an interjection is inserted in the middle of a sentence, between commas, it can be considered a parenthetical element as mentioned in one of the comments.
However, to answer your question, ("what about when the aside is an interjection?") when the aside is an interjection, simply call it an interjection, no matter its position.