I've searched but I haven't found anything on this cube.

I try to solve it like a 3x3x2 first solving the middle layer and then solving the 2 adjacent layers. But I don't seem to be able to do it like that. Most of the time, the right part of the inner layer ends being twisted 180 degrees.

Can someone give me a tip on how to solve it?

You should be able to look up a 3x3x4 parity algorithm, just apply every u turn to every slice that has the parity.

The parity algorithm is slightly different to the normal 3x3x4 algorithm because you will be applying it to an odd number of layers, whereas the 3x3x4 algorithm only works on an even number of flipped pieces, although the difference is minor.

Assuming that you have solved the first 2 layers around the centre, apart from the flipped side here is what you do:

spoiler
[The algorithm is U2 R2 F2 U2 F2 R2 U2 F2

Where the U layer is the layer above the the first flipped piece, so the second layer from the top in your case]

edit: I forgot to mention that you need to have the flipped face as your front face when performing the above algorithm, so the pieces that need to be swapped are on the left and right of the front face

Marty, your algorithm works, but only when I'm solving the second layer from above. If I'm either in the third or the last layer, it doesn't work.

first get it back into cuboid form while doing that insert a cross for the inner most pieces and fill in the edges in the correct place as a normal 3x3, once solved as a 3x3x2 do it as if it was a 3x3x5 then again to solve for a 3x3x7, watch my walkthrough of my 3x3x5 but then repeat the steps for the extra 2 layers
https://www.youtube.com/watch?v=eyFbsHrs-uY sorry im not very good at explaining, the video might help

in that case you just need to use a different layer as the Up layer - for the U turns, use the layer above the first piece that needs to be switched, as long as all the pieces need to be switched.

If you only have the parity problem on one layer then the algorithm is:

Spoiler [ Uu2, R2, F2 Uu2, U2, F2, R2, Uu2

Where Uu2 refers to the top half of the flipped pieces and any/all layers above it]

Believe it or not, I actually found it quite easy to solve it by conjugates and the Rubiks website algorithms, matching up the corners then the edges. Is that too much of a spoiler?

Also, what are the parities everyone keeps mentioning?

When solving this or other cuboids similar to it using 'normal' cuboid algorithms (i don't really know how you've done it) you often reach situations where you have 2 pairs of edges pieces that are swapped after finishing all the other pieces in a particular pair of layers, the parity algorithm fixes this