They were terrified by it. My son has been pestering me to watch a scary movie with him for a long time. This will probably stave off that desire for awhile.
I understand your wife's position, but have you considered starting them out with old B&W horror movies? Maybe Vincent Price since he narrated 'Thriller'. The oldies are spooky but not gory. Also, profanity is minimal to non-existent. The worst you will get is an occasional 'damn' or 'hell'. 75% of modern horror is gore and sex; that is not an issue with the real classics.
This still gives me the heebie jeebies and I really wish it didn't. I still get nightmares about it. The one about a Thriller ghost train still seems to be the biggest recurring dream.