If you both are using the same Apple ID for iCloud (not a good idea) and you both have iCloud Photos turned on, all of your photos will sync to iCloud and to each other's devices. The only way to prevent that would be to turn off iCloud Photos on one of the devices. If you decide to do that, see instructions in Get help with iCloud Photos - Apple Support
I'm not aware of any way to stop phone history from syncing when two iPhones are using the same Apple ID for iCloud.
Also, be aware that you could each have your own Apple ID and still opt to share selected things such as purchases by using Family Sharing: Family Sharing - Apple