This thread, and below, will explain to you how to solve this mystery. Some people may have heard that it is impossible for factions in Single Player. But those people are wrong!
The Cause: You have not defined the factions correctly for Single Player. It will show up in Multi Player because you have defined them correctly using 'mpnewcharacter.fl'.
Modding a '.fl' file is not that hard once you have the correct software and a knowledge of editing 'mpnewcharacter.fl' and other '.ini' files. All you need to begin with is a Freelancer Saved Game File Decoder. I could suggest one but it cannot convert back to Encrypted message once it is decrypted. So it will stay readable forever.
If you want to securely hide the contents of your '.fl' file then you should not use the one i am about to give you. Use another one created by somebody else that can be found on the forums. But, like me, i like to keep things readable to all factions (Humans).
The program is created by the author of the famous mod activating and deactivating utility of all, Freelancer Mod Manager: Matthew 'IGx89' Lieder. The file is called FLS1 and can be downloaded from this site. It does not show up on any of the search databases for some reason but i will give you the link:
FLS1 <--- Link.
These are the tools you'll be needing in order to proceed with this tutorial:
Any INI editor. QuickFix is good.
Any Freelancer Saved Game Editor. FLS1 is good.
Read below for the actual tutorial.