A simple approach would be to do it on the fly, concatenating lines if possible, otherwise proceeding with working on them.

The approach I use most often is a tip i found from one of merlyn's posts - use a buffer:

use strict;
use warnings;
use autodie qw/open close/;
## buffer for holding current text;
my $buffer = '';

open (my $fh, '/foo/bar.txt');

while(<$fh>) {
    ## clear trailing whitespace
    chomp;
    if (/\/$/) {
      ## use regex to see if line ends with a slash
      ## append to buffer
      $buffer .= $_;
    } else {
      ## it's a single line so just process
      process($buffer); ## sub elsewhere...
      ## reset
      $buffer = '';
    }
}

close $fh;
[download]

NB: Not tested! Just example...

Update - This is merlyn's node - Re: Reading multiple lines?. Maybe not quite the same thing, but it inspired this response, or at least was the first place i came across this kind of control structure... He also remembered to check for the 'end of file'...