In these situations, I come up with a way to read one "record" at a time. You can do several things to get back all of the information for one record with one operation.

For instance, write a function to read two lines at once (adding appropriate checks I don't cover here).

while( defined( my $record = get_record( $fh ) )
    {
    # ...
    }

sub get_record
    {
    my $fh = shift;

    join '', scalar <$fh>, scalar <$fh>;
    }
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Sometimes preprocessing the data works better. You take your data file and join the appropriate lines. It's even better if you can track down the guy who can change the output at the source. :) Once it's all on one line, life is easy.

A red line is found at location 2.5 4.5
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I've also found alternate delimiters useful. If you have to have a newline between the two interesting lines, maybe you can have a form feed (or something else) as the separator between records. Then you can set $/ to the record separator and read records instead of lines.

A little database is a little more fancy than that, and more useful if you have to use the same data file over and over. Process the file once and store it in something such as a DBM::Deep file. Now lookups are as easy as using a hash, and you only have to process the file once.