I didn't apply to UCLA, but typically the way this works is that if either the school or the department turns you down, then you're not invited at all.
The school looks at your academic record and test scores (the statistical garbage) and decides if you meet the overall school requirements. Then, if you do, your application gets passed on to the specific department (in your case, the film department). The department then evaluates your application.
So the way to look at it isn't as two separate applications. Just one application that has to make it past two parts of the same school. This is why, when you mail in your application, some of your materials get sent to the admissions office and some get sent directly to the film department.
But not all schools work the same way. At some schools, the department makes all of the decisions. The only way to know for sure is to read all of the material on the school website about admissions procedures. Usually the process is pretty clearly outlined.
Good luck. Long live Chicago.