A very interesting question - I had to think about this for a bit, but my conclusion is that the sentence is not in the passive voice.
A passive construction has a subject that is the recipient of an action. For example:
Passive voice: Big Bird was seen by many people.
To put this sentence in the active voice, you turn the sentence around: Many people saw Big Bird.
However, the example you gave, the subject "I" is not the recipient of the action "invested". No one/nothing "invested in me." You *cannot* turn "I am now emotionally invested in this" into "this now emotionally invested in me."
Instead, "I am emotionally invested in this" is in the active voice with a participial adjective. In other words, "invested" serves as an adjective, just like, say, "happy".
Compare: "I am emotionally invested in this" vs. "I am happy about this." These are both in the active voice.
A little note: We say "emotionally invested IN" something, not "WITH" something ... :)