Do fishes have 3D vision?

Short and tricky answer, yes. It is tricky because fish are a vast number of animals, besides a paraphyletic group of animals.
Long answer that need an explanation i´ll provide you bellow is "yes, to some degree, fishes are able to have binocular vision".

Getting into a deeper view of your point, what you are looking for is binocular vision. And it is due to the superposition of the fields of vision of both eyes and the work of the brain as you say.
And you are right, the position of the eyes have a a determining role on getting this binocular or stereovision, exactly they inceed in the width or degree of the angle where this 3d vision is possible.

• For a start, we can take a look to a typical hervibore mammal. I choose this protoptype because they live in the same enviroment that we do, and they have similar eyes to that we have:

The Mammal Eye and Vision in Mammals
Horses can see up to 215º, but have a binocular vision field of less than 90 degrees, just in front of their head. Humans have a total vision field of 180º, 140º of binocular vision.  In fact, primates have greater binocular vision field than typical carnivores. This is a great advantage if you jumping between branches and can fell down more than 40 mtrs if you don´t see clearly how far is the next branch.

• Let´s go to the fishes. They make stereovision the way we do, overlapping the two eyes field of vision

The Earth Life Web, the Fish Eye and Sight in Fish

• But many fishes have an extra vertically flattered head that keep their eyes quite in the side of the head. One of the ways of improving their frontal, and thus binocular vision, is to increase the their monocular field of vision.

This chart is excerpted from The Earth Life Web, the Fish Eye and Sight in Fish

                     Visual Range in Men and Fish
 Entity Horizontal Vertical Binocular
Man              154°              150°              25°  
Fish                165°             134°               12°                          (**)

This is what many of the fishes that have extra narrow compressed head  shape do. They usually have very large eyes and they are in a very front  position in their heads, allowing a major overlaping this way.


(**) You can say now, but you telled that people had 140º of binocular vision. Yes, but here are data from another source and they make a difference between horizontal and vertical vision. And data usually varies a little depending of the source.


As usual, predators have more frontal eyes to increase distance perception and prey side eyes to increase the field of vision in spite of binocular vision.

• There are more special adaptations to improve their vision skills as water is a more challenging enviroment to this sense that is air.

• Some of the deeper water fish have tubular eyes with big lenses and only rod cells that look upwards. These give binocular vision and great sensitivity to small light signals. This adaptation gives improved terminal vision at the expense of lateral vision. Vision in fishes.

• And there are more tricks in the bag: Benthic

• predators, like flatfish, have eyes arranged so they have a binocular view of what is above them as they lie on the bottom. Vision in fishes.