A schizophrenic ex-serviceman wants to revenge his imaginary wife and her lover!

"The ?big reveal? is a cliche that has been used many times ? ?it was all a dream??" Yes, this is true.
But rather than have it be a big reveal(since it wouldn't be that surprising due to the schizophrenia) I think it would be much more interesting to have him constantly questioning whether what he is experiencing is reality or imaginary.
But what is the plot? He's a veteran, certainly he could easily kill his wife, and her lover, whether in his imagination or reality.
Just a thought, you could add a "Mr. and Mrs. Smith" type feel to it, so when he goes to kill his wife, he finds out that she is an agent/spy/soldier.
In order to incorporate what I said above, leave out that his wife is imaginary altogether, mentioning schizophrenia will insert that doubt.
Anyway, you have his goal, now what does he do to achieve it?

When I read your original logline I thought it was a comedy.

If you want there to be a big reveal, perhaps try something like this:

Cuckolded, an ex-serviceman seeks revenge on his wife and her lover only to discover the impossibility of the task.

The 'big reveal' is a cliche that has been used many times - 'it was all a dream'...

If you want to tell a story about a person with?schizophrenia, perhaps try to come up with another way of dealing with the imaginary v real element. What if he is aware of the imaginary people being imaginary? What if he's fallen in love with an imaginary woman and prefers her over his wife?

I don't mean to be a downer, but the idea of a "big" reveal in the end that it was all in his head has been done so many times to the point that?it may work against you.