Actually, even with Intralink alone, this type of permission set would not be possible. The only way you could achieve this with PTC products is with a combination of Intralink and Toolkit. Toolkit could provide the extra check of 'file type' that you are looking for.
Without these, it gets alot more 'creative'. You could do it in a windows environment by placing each file type in a different top-level folder, and then assign permission to these folder in the classic Windows fashion. Of course, you would need someone to monitor/administrate these folders and ensure that the correct files are placed into the correct folders.... can anyone say nightmare! I guess you could have some sort of program/script that did the majority of this for you - whenever a .drw is created, it is moved to the drawing folder, etc.
Maybe if you expand on why certain people would have access to parts and not drawing or vice versa, it may help in a solution. Keep in mind things like the following... If a person has read permission on drawings, then they MUST have it on parts/assemblies, because Pro/E needs to load them into RAM in order to open the drawing (I know there is a way around this, but you get the idea).
Good Luck,
Richard