I did it for years and never had a problem with disease.
Here are the things you will need to plan for.
1. Nest boxes need to be up high and the opening too small for chickens to enter.
2. Roost poles for the pigeons need to only accessible to the pigeons or the chickens will take over and keep the pigeons from roosting.
3. Food and water follow the instructions above.
4. I also cut a pigeon hole with door in the human door so the pigeons could get out and away from the chickens if they wanted. This however turned out to be the downfall for my pigeons. Although I probably had pigeons for 8 years and never a predator problem a cooper's hawk showed up and within three months all 12 of my fantails were taken. I was actually down to my last pair and never let them out unless I was around, well one Saturday I opened the little pigeon door as I was planning on be out for about an hour or so (my birds usually only came out to exercise their wings for about 20 minutes or so and head back in) and right as the first pigeon came out and took off out of no where swooped this hawk, basically right in front of me, caught the pigeon and disappeared in the distance.