Hi Mau and welcome to the forum.
What a mixed blessing of an inheritance when you took on the flat, but well done to you for giving things a good try.
Who currently feeds the cats and cleans out the litter tray? I would say that if it's you, then you need to abdicate these functions and let your husband be the one who gets those jobs. The cats have to begin to associate him with the good things - the food, the home comforts. It does sound as if they've had a bad experience with a man (possibly their former owner) or they're still upset about the changes generally.
They need to be able to associate your husband with fun and treats. I would also suggest maybe getting a flying frenzy toy (Purrs shop sells them) and instigating some play sessions. Most cats will really enjoy these prey substitute fishing rod style toys, and its a great way of engaging their interest, especially if you can persuade your husband to really go for it when he plays with them - think about how prey would normally move, and try to mimic the fits and starts, or a bird in flight. It's really important too that they get to "keep" their prey at some point in the play proceedings, or to get a reward once they've "killed" it. Your husband may need to practice his technique, but if he starts small and sees how it goes, it could begin to get results within a relatively short period of time.
Do you have piccies of the cats, and what are their names?