刘老师的解答是正确的。

本句中，deeply invested in与前面的well balanced, mature, caring并列，都是 不定式to be的表语。所以invested是及物动词invest的过去分词演变而来的形容词，虽然词典没有收录这个形容词。

《韦氏学生词典》invest作及物动词词条下的释义和例句如下：

[+ object] : to give your time or effort in order to do something or make something better — usually + in

• A lot of effort was invested in the project.

• We need to invest more time in educating our children.

• (chiefly US) She is deeply invested in this project [=she has given a lot of time and effort to this project and cares about it very much] and wants it to succeed.

红色字体的例句中谓语就是系表结构，不是被动语态，和你提问的句子中的invested的用法是一致的。