How To Prevent My Monkey And Parrot From Fighting?

I like to walk with my parrot on one shoulder and the monkey on the other. They are great accessories for when I visit the park because lots of women will come up and talk to me. But the problem is that my monkey hates my parrot.
I believe the reason for this is that when the monkey opens his cage and starts doing mischief, the parrot starts screaming his name and I hear and catch the monkey and put an end to it.
So when they are on my shoulder, the monkey will reach around the back of my hear and slap the parrot off or pull its feathers.
My parrot is so stupid, it thinks that because my face is next to it, I have to be the one pulling its feathers and he gets mad and picks me on the ear. One time it bled!!!
Another time my monkey was throwing his faeces at the parrot when the parrot was on his perch.
How can I get these two animals to get along better?