Since we just had an eclipse, I began to think: what would it look like if a planet had rings and two moons?
Now, there are two solar eclipses going on at the same time! What would the sky look like?
I saw in another question that the rings give off their own shadow as well, but regardless of that the question remains:
What would the sky look like if the planet had rings and was experiencing a double eclipse? By double eclipse, both moons are causing an eclipse at the same time.
The rings, in a stable system, will be on the same plane where the eclipsing moon is orbiting, so at least part of the rings will be in the shadow cone.
If eclipse is not projected in the above plane (i.e.: sun is not exactly on that plane, also), shadow cone will leave the rings and won't cut the whole rings but only make a dent in them, if the moon is farther then remotest ring effect may be null ("dent" may terminate before beginning of rings).
In any case you would see, more or less, what you see from Earth.
If the moon is really big (like ours or more) and the eclipse is total you could see the rings even by day, in spite of the refraction from the atmosphere.
You could be able to see a dent in the ring, but that would be doubly difficult because the gap would be exactly where the sun should be, so any glare and/or refraction will cover it making it impossible to discriminate.
The effect would be evident if observed from space, possibly from a point relatively far from orbital plane.
It is unclear to me what you mean, exactly, by "double eclipse", so I cannot answer that.
There are many other factors determining how it looks which you haven't mentioned. The time of day, the axial tilt of the planet, the observers location, etc. Note that the moons will be orbiting within the ring plane, and so the shadow of the moon must lie along the intersection of the ring plane and the planets orbital plane.
In general, I think the most spectacular view would be that for an eclipse crossing the equator and directly overhead. In this case, the rings would appear to come out on opposite sides of the sun/moon, directly overhead, and those parts of the rings will be illuminated. The amount of bounced light and indirect illumination is debatable, as is indirect bounced light from the other moon, but it might be possible that the sky darkens as much as in our eclipses, with the rings being like a glowing thread stretching down to opposite sides of the horizon. It's also possible that the outer rings would be illuminated, but obscured by the dark inner rings, so that the entire ring structure would be invisible.
A little further away, to the north or south, the face of the rings would start to become visible. The sun will be illuminating the rings edge-on, and so indirect illumination on the ground should be minimal. This means the sky wouldn't be fully dark, but pretty dark, and the rings wouldn't be all that visible, but if they were, the shadow across the rings from the moon would make the rings look like they had a gap in them, to observers outside the eclipse zone. The observers in the eclipse zone probably are too edge-on to the rings to see much.
For eclipses occurring not on the equator, for an observer not on the ring plane, and assuming the planet has an axial tilt (seasons) then the eclipse could look like ours, but with the addition of rings, a bit like a thin or dim rainbow, with the outer ring illuminated on the sun side, and the inner rings mostly unlit.
