First I'll try to give my advice, or rather what I would do if I really find myself in that situation. I also added some folklore and beliefs from the older generation of my country I was reminded of when I heard this story for the more enthusiasts of the subreddit.

Don't act rash and stupidly, jumping into belief after a belief. Act rationally. (As if that was not obvious though.)

1. If I were in that scenario I would definitely leave the house. Convince your husband to do so. (I believe he is the victim of this situation, so if you are powerless against it, save yourself first and immediately seek help. Maybe call your friends to drag him out of the house but don't do anything stupid.)
2. Seek religious help. Religion always heals your mind when it comes to unexplainable things.
3. Also seek psychiatric help. Your husband really needs that and also you may want it too after the whole experience.
4. Talk to your parents/siblings/loved ones/trustworthy friends about it. It helps a lot.

And here's that folklore if you want.

I'm a Sri Lankan Buddhist and here the older generation including my parents believe sometimes when people die when they are experiencing negative emotions such as lust for something (maybe even the house or a family member), fear or hatred or if they committed sinful deeds, they will be born in the afterlife as spirits, who we call "Pretha" (Details: https://en.m.wikipedia.org/wiki/Preta) or "Kumbaanda", where they become somewhat connected with the said house or member. Most of the time, as they say, these spirits are not harmful (they are enduring suffering themselves as they say these spirits live in extreme hunger or thirst) and cannot be seen by human eye, but sometimes they let their presence be known often for past family members or close relatives (even from another past life) or if the victim is somewhat lacking of merit in their life. When that happens our elders either commit merit as our religion says like alms giving or a Pirith chanting(What is Pirith: https://en.m.wikipedia.org/wiki/Paritta) or (at least they used to) resort to ancient exorcism rituals called "Thowila." (More info: https://en.m.wikipedia.org/wiki/Demons_of_Sri_Lanka)