I wrote a post a while ago about the undocumented $assignments function, which allows you to get access to the assignment file settings that you are currently using, but this doesn't help you get to the filename itself.
One suggestion I've seen before is to add a logical to each assignment file which specifies the name/location of the file. However, it's way too easy for someone to move, copy or rename the file and neglect to update the logical, and then worse than not knowing, you think you do know but the information you're being given is inaccurate.
Luckily Uniface 9.6.06 has solved this problem with a new undocumented feature of $processinfo...
This will put the command line used to access the application into the message buffer. For example...
"\\server\location\uniface\bin\uniface.exe" /asn=\\server\location\adm\uclidev.asn /ini=\\server\location\ini\me.ini APPSHELL
As you can see, the assignment file and ini file are both specified in the command line, along with the application shell as well. This should give you all the information you need, although you'll need to do some string manipulation to pull out the bit(s) you want.
This was recently discussed on the UnifaceInfo.com forums, so you can check there for more context, and sign up if you haven't already!
Summary: You can access the current assignment file location, but accessing the command line, as long as you're happy to use an undocumented/unsupported feature.