Hello everyone,
I have this problem since I bought some headphones with a single jack for both input and output. My Asus F556U laptop has a single jack for both input and output too.
When I connect them, output on them works flawlessly, while input keeps being provided by the laptop internal microphone. Alsamixer only has one "Capture" volume control, as well as Pavucontrol and the GNOME sound settings.
On Windows the headphones work (I had to install an additional Realtek driver for my sound card, though).
The current distribution is Fedora, but since the moment I bought the headphones I've been switching to different Linux distributions, including Ubuntu, Manjaro, openSUSE and Arch, and none of them seemed to make the microphone work.
I also found some "hdajackretask" hack somewhere on the net stating that I should run hdajackretask and override pin 0x18 to "Microphone", but it doesn't seem to work.
Any help would be greatly appreciated.

Some boring hardware help first: how many pins are on the plug? Talking from the tip of the plug, there's usually three.
1. left
2. right (or possibly the reverse order)
3. (nearest the plastic) Common negative.

This above socket is usually coloured green, and is OUTPUT. There should also be a 3.5mm pink socket with 2 lead plug which is INPUT
1. Mic signal
2. (nearest the plastic) Common negative.

This plug and socket are usually pink. Have you got both sockets as I describe them, and both plugs?

Here's a photo of the plug: https://imgur.com/a/b2v8c
It looks like it's the same way you described it.
The socket is just one as well, I don't understand what you mean. It's a single socket for both in and out.
However, I think it's a software problem, since it works on Windows.

OK - that's a 4 pin socket
1. Left
2. Right (or mebbe reversed)
3. Mic
4. Earth
If they're BOTH 4 pin sockets - no problem. Is it set up in your alsa config? Alsa has the drivers, Pulse is just the frontend; you can run alsa without pulseaudio (As I do) but not pulse without alsa.

I don't know whether it's setup. I certainly didn't set up anything about it. Could you please explain me how to do it? Thank you very much.

Okay, somehow I managed to get it to work! Thanks to your help, I found this page (http://www.alsa-project.org/main/index.php/HDA_Analyzer), I downloaded the program, started it.
Then I went (on the left) to "Node (0x23) AUD_MIX", unmuted Val[2] and Val[3] and muted the other two which were enabled. Then the microphone worked; it still doesn't work if I disconnect headphones and connect them again, or if I reboot. Is there some way to solve that?

I think you may need an ~/.asoundrc or /etc/asoundrc by which means you can specify stuff to alsa. I'm not hot on it myself; I did get assistance with hdmi sound resampling my 44khz o/p @ 48khz, which stopped it sounding like it had been through a food processor.

You may just have to select your sound source in your recording software.
(I use audacity.)