If they're as close to a decently-sized black hole as dramatic movie pictures require, I suspect they would be close enough for the separation not to be gentle at all, assuming their individual limbs wouldn't separate.
Jupiter density: 1.33 g/cm³, escape velocity: 59.5 km/sec
I think it's more than just density.
In case of mostly anything else, Newtonian physics apply correctly, and the relevant thing is mass (and distance from the center). The escape velocity from a body is sqrt(2GM/d) where d is the distance from the center of mass, M is the mass of the object, and G is the universal gravitational constant.
Note that if the sun was replaced with a black hole of the same mass, the orbit of the earth wouldn't change.
I wouldn't be surprised if that's in the script somewhere but ended up on the cutting room floor.
And in case of "blowing up" they could use those am engines as LAS (they apparently had enough thrust), so what risk are you speaking about?
Seriously, bitching about science stuff in Interstellar, very large but actually very well crafted scifi is kind of dumb. It's big enough that you find SOME mistakes, but most of the time you'll be wrong (or blaming them for not explaining every detail), and it has pretty correct science overall. Just hating for sake of hating.
Plus, the ship's engines don't appear to use propellant - they use the standard sci fi "eeire blue glow" trope. Seems like antimatter is the best explanation to me.
Also, he had Kip Thorne as an advisor. I remember criticism of the "slow-time planet" (including by Bad Astronomy) being shot down by Kip pointing out he actually calculated it as an edge-case solution for a specific rotating black hole.