
I had the same situation when I got my first 2 dogs.
To be honest the pups took a full 6 months to realise that there were a couple of cats in the house as they caused such a rumpus on a daily basis that the cats stayed out of their way and just watched from the sidelines. Once they did realise then they did want to chase.
However from day 1 my pups were not allowed in the kitchen (where the cats ate) or the bedrooms (where the cats slept) so the cats always had a safe haven or two. That was when we lived in a bungalow, now we are in a 2 storey house so the dogs are just not allowed upstairs.
I am never going to have a family of animals that love each other and sleep together but they do sometimes sniff noses and mix briefly when supervised. It's up to the cats if they want to mix but it's easy for me to separate them as my cats both became house cats once past the age of 10 and they just like to sleep upstairs most of the time.