The appearance of the black hole in Interstellar was not created arbitrarily. It was actually modeled using the real relativistic equations describing the path of light in the gravitational field of a super-massive black hole spinning at near the speed of light. As a result, it may be the most accurate depiction we have to date of what such an object might look like. Astrophysicist and gravity expert Kip Thorne collaborated with the visual effects team to produce new software specifically to model the equations and render the black hole. The appearance was initially somewhat unexpected, but Kip Thorne realized "Why, of course. That's what it would do."
I don't pretend to be an astrophysicist, but on a basic level, here's what's happening: The glowing accretion disk of plasma remains in a single plane as expected (there's no perpendicular ring), but some of the light from the back side of the disk is warped by the intense gravitational field, over the top and bottom of the black hole. Thus in the region just outside the black hole, you are actually seeing around to the back side of it.
Indeed, the discoveries made during the rendering process has even led (or will lead) to the publication of several scientific articles on gravitational lensing.
There's more detail, including a video with Kip Thorne describing the effect, here:
Filmmakers often use a technique called ray tracing to render light
and reflections in images. “But ray-tracing software makes the
generally reasonable assumption that light is traveling along straight
paths,” says Eugénie von Tunzelmann, a CG supervisor at Double
Negative. This was a whole other kind of physics. “We had to write a
completely new renderer,” she says.
Von Tunzelmann tried a tricky demo. She generated a flat, multicolored
ring—a stand-in for the accretion disk—and positioned it around their
spinning black hole. Something very, very weird happened. “We found
that warping space around the black hole also warps the accretion
disk,” Franklin says. “So rather than looking like Saturn's rings
around a black sphere, the light creates this extraordinary halo.”
That's what led Thorne to his “why, of course” moment when he first
saw the final effect. The Double Negative team thought it must be a
bug in the renderer. But Thorne realized that they had correctly
modeled a phenomenon inherent in the math he'd supplied.