A PCB/pinheader question

I put my I2C interface on my 20x4 display in what I thought was the correct way, but it ended up not working correctly....

I looked at this picture

and I decided that putting it on top but with the pins in the same position would work.

But then it didn't work, so I guess the question is, do pinheader holes act like vias in that both sides of the PCB in that hole are connected, or is each side not connected to each other other at all? I always thought they were... but now I'm having doubts and am wondering if that's why my LCD wasn't working...

So was my assumption:
"putting it on top but with the pins in the same position would work."
incorrect?

The pins go straight through the holes.

Pin holes are usually connected top and bottom of the board.

The problem with many PCBs is that they are not adequately marked.

LCDs are usually connected via a "standard" pin layout. Pins 1 to 14 are the usual numbering. Your I2C board should have some marking to relate to that system.

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