I am using the Iceweasel browser (derived from Firefox) on a Debian system with the XFCE4 desktop.
I did not define any custom font substitution in ~ / .config / fontconfig / fonts.conf.
This is what fc-match tells me.
lone@debian:~$ fc-match "Liberation Mono"
n022003l.pfb: "Nimbus Mono L" "Regular"
lone@debian:~$ fc-match Courier
n022003l.pfb: "Nimbus Mono L" "Regular"
lone@debian:~$ fc-match monospace
DejaVuSansMono.ttf: "DejaVu Sans Mono" "Book"
Therefore, I expect that when I have HTML, the font "Liberation Mono" should give the same results as when using "Courier". But, as you can see in the screenshot below, this is not the case (JSFiddle: http://jsfiddle.net/8L3rmyxn/ ).

I clicked the "Check item" button and found the fonts used.
, "Liberation Mono" CSS, "DejaVu Serif" , fc-math.
"" CSS "Nimbus Mono L" , fc-match.
, "monospace" CSS, "DejaVu Sans Mono", fc-match.
"Liberation Mono" "Nimbus Mono L" "DejaVu Serif" ?
, . " " ~/.config/fontconfig/fonts.conf, , " " "" .
lone@debian:~$ cat ~/.config/fontconfig/fonts.conf
<?xml version="1.0"?>
<!DOCTYPE fontconfig SYSTEM "fonts.dtd">
<fontconfig>
<alias>
<family>Liberation Mono</family>
<prefer><family>Nimbus Mono L</family></prefer>
</alias>
</fontconfig>
lone@debian:~$ fc-match "Liberation Mono"
n022003l.pfb: "Nimbus Mono L" "Regular

,
. fonts.conf, "Liberation Mono" CSS, "Nimbus Mono L" "DejaVu Serif" , fc-match "Liberation Mono" , , fonts.conf ?