Transparency problem on some faces when overlapping regardless of normal

Hi!

I'm having the following problem: When setting transparency for a specific 3D mesh, some faces are fully invisible when viewed through an overlapping side of the same object (screen-shots below). When no transparency is used, the object is shown normally. This result comes from using the standard Unity shader, but as a final result this specific object should be using a double sided transparent shader (which I think I got figured out). I tried flipping, recalculating the normals, modifying the object(thickening/smoothing/deleting faces and remaking some) in Blender but with no success whatsoever. Can someone please help me figure this one out?