I have just painted mine with Sandtex masonary paint. I have only done the outside surfaces. I have left the joining surfaces alone. the only thing I have done inside is paint the slopes sides in the food tray and put some sand on it to give the girls a helping hand.
I would have left it totally alone but I read on here that the paint protects the Poly from the ultraviolet rays. Not that we have much at the moment.
I normally paint the bits where the boxes meet and in an unsupervised moment my husband painted the insides as well of one of them. It's been fine though so I wouldn't worry either way
We painted the bits where the boxes sit on top of each other, they are Masie, they don't stick with Dulux weathershield but do with certain colours of Sandtex, we found it depends on the paint!