Bought my mom a house with that old, avacado green, sculpured nylon carpeting. Thought I'd just tear it up and toss it. NOPE! Ran into the same problem you're having, only the pad had "glued" itself to the plywood subfloor. Years of "steam cleaning" and center-of-the-floor traffic had comrpressed the pad to something like thick cardboard, and huge sections were stuck TIGHT.
After pulling the 3 million staples with a needle nose plyers (this is the hands-and-knees part), I used a floor scraper (looks like a long-handled gardening hoe, only the blade sticks straight out from the handle) to removed the stuck-on padding (this is the backbreaking part).
Of course, some of the really tough places were still stuck tight, so dawning a respirator (important!), I went after them with a belt sander. That did the trick.
I seriously doubt you will have any luck salvaging the lino underneath this carpet padding, but then, as Ron says, it will be full of staple holes, so why would you want to? Have fun.