Here's how I might do it (if I understand you correctly):

#!/usr/bin/perl

use strict;
use warnings;

use File::Copy;
use File::Find;
use File::Spec;

my $source="your_source_dir";
my $dest="your_destination_dir";

my $abs_source=File::Spec->rel2abs($source);
my $abs_dest=File::Spec->rel2abs($dest);

print("Source directory: $abs_source\n".
      "Destination directory: $abs_dest\n");

sub fileprocess{

    print("Processing file: $_ ($File::Find::name)\n");

    my $rel_file=File::Spec->abs2rel($File::Find::name, $abs_source);
    my $dest_file=File::Spec->rel2abs($rel_file, $abs_dest);

    if (-d $_){                # deal with directories as special case
        mkdir $dest_file or die("$!\n"); 
    }else{                     # copy the files
        copy($File::Find::name, $dest_file) or die("$!\n");

        # change the permissions to those of the source
        my $mode=(stat($File::Find::name))[2];
        chmod($mode, $dest_file) or die("$!\n");
    }
}

sub postprocess{
    my $rel_dir=File::Spec->abs2rel($File::Find::dir, $abs_source);
    my $dest_dir=File::Spec->rel2abs($rel_dir, $abs_dest);

    # change the permissions to those of the source
    my $mode=(stat($File::Find::dir))[2];
    chmod($mode, $dest_dir) or die("$!\n");
}

find ({wanted      => \&fileprocess, 
       postprocess => \&postprocess}, $abs_source);
[download]

Update:Bug fix - the original code would fail to process files in a given directory if the user did not have write permission for that directory (which is what you want to do...duh, silly me). Fixed using the 'postprocess' feature of File::Find to adjust directory permissions after processing the files in that directory.

Good luck,
Tim

Update2: I just noticed that the perlmonks documentation on File::Find appears to be incomplete. Check out your local 'perldoc File::Find' or go here.