Definition of “infix” in formal languages
Yes, if $A$ is the alphabet, then $L = A^*aabA^*$. 

Now, what about terminology?
Lothaire in the first chapter of his book Combinatorics on words gives the following definitions. A word $v \in A^*$ is said to be a factor of a word $x \in A^*$ if there exist words $u, w \in A^*$ such that $x = uvw$. A factor is proper if $v \not= x$.

In my opinion, the word infix is also perfectly fine, since it gives a natural counterpart to prefix and suffix. Terms involving "sub" like subword and substring are also frequently used in the literature. I personally prefer to follow Lothaire and say that a word $v \in A^*$ is a subword of a word $x \in A^*$ if $v = a_1a_2 \cdots a_n$ (where $a_i \in A$ and $n \geqslant 0$) and there exist $y_0, ..., y_n \in A^*$ such that $x = y_0a_1y_1a_2 \cdots a_ny_n$. This definition makes the term subword a synonym of subsequence, which I find quite natural.

Anyway, with so many different terminology around, it is not a bad idea to remind the reader of precise definitions if there is any risk of ambiguity...