I've got two cats and a 7 month old puppy - they're not exactly integrated...
I've got a 10 yr old Siamese and a 2.5 yr old moggie, we had a dog until about 2 years ago, the Siamese always lived with him quite happily, but mistly ignored him, the moggy arrived as a tiny kitten, took a couple of weeks to stop being terrified of him, but then was his best pal. He died when the moggy was about 6 months old.
The Siamese was never phased by meeting dogs outside, the moggy was terrified and figuring that the Siamese was used to dogs and the moggy would have forgotten our old one it was the moggy we were worried about introducing the puppy to.
The cats have free reign over the entire house, the puppy isn't allowed upstairs, so they have somewhere to go if they need to and they're allowed on the couch and he isn't (he's too big, lol). I also moved the cat food up where he couldn't reach it. He's crated when I'm not there too.
What's actually happened is that the Siamese wasn't bothered when he arrived and seemed to suddenly realise that he was here to stay after a few weeks - since then she's decided that he shouldn't exist in the same house as her and randomly attacks him if he's in reach...he just looks at her a bit perplexed and avoids her.
The moggy spent about a week stalking him, looking at him like she might eat him, then suddenly went all friendly. Because she rubbed up against him a few times, he's obsessed with her, he follows her round trying to squash her with his big head and paws so I have to keep him away from her, which results in him staring at her from across the room longingly, because he luffs her sooooo much, lol.
So not integrated, but nobody is too stressed, except the puppy who just loves them both from afar.