Stripping wallpaper that had been painted is pretty much the same as stripping unpainted wallpaper. The difference that it's just going to take a bit more perseverance to get it off.

The main technique to getting wallpaper off is to break the bond between the paper and the original wall surface. Steam, wallpaper remover, moisture all require that it can penetrate through the paper to the adhesive that holds it to the wall. When dealing with painted paper, that process just becomes more tedious but doable.

I stripped some paper that was painted and then "textured" with some dry wall compound. Like you I discovered it as it started peeling and creating issues. I used some standard processes and the paper came off but it took a bit more elbow work.

Here is a link that might be useful:

Yours is the classic example as to why you DO NOT paint over wall paper.Removal now becomes a little more involved as posted , but doable.

Here is a link that might be useful: removal

I've seen it more times than I care to remember, especially on nasty ceilings, where somebody decided to paper over hair-line cracks, and then somebody after that decided a paint job would do for awhile. argh

Sometimes, as you said, the multiple layers of paint give the paper body, like papier mache' and make it easy to pull it off intact. I have seen some drywall finish come off with it. I guess you would have to see how much damage that leaves the drywall, and decide whether you would rather do a skim coat, or be very careful with the steaming off the layers.