By any chance is the first row the column headings? If not any chance it can be made to? If so there is a setting on the connection manager that will tell it to use the first row for column headings and that should resolve your problem. If that won't do it then you will need some way for the package to tell the difference between the files. Either by name of the file, or by the contents of one of the columns. I've dealt with a file that had 6 different types of rows in it and the first column was lettered a-f to tell me what it was. That isn't to hard to deal with.

If you can't get the column headings in the file then see if you can tell me how you tell what columns are in the file then we will see what we can do :-).