I should point out that both of these machines are virtual machines, in case that alters anything.
Actually that can be a problem. If these VM's are on the same machine the as long as
you have matching network configurations both using with or without NAT. Then you
should be able to ping each other.
The question I am not clear on is the file you wish to expose. Is just a file or a web page.
You could use filezilla which iirc can do ssh and then browse the shares on the Linux machine.