Here is a regex solution just for fun:

use strict;
use warnings;

my $data = do {local $/; <DATA>};

while ($data =~ /^(john.*)\n(?:(?!john).*\n)*?(jacob.*)/mg) {
    print "$1 > $2\n";
}

__DATA__
bhgfsggdsgsg
--
john1
weruwearnwrnweuarar
jjafdaiuweifweofiuwe
jacob - 1.0
--
nfaslf23523525
john2
asfsjldf43tgre
john3
asbdfhskafbv3333v
sdfahh34ttg
sadfhk34t3wtg
sdfhk3gfwghhw3
jacob - 2.0
[download]

However, I'd also advise line by line processing for this type of problem.

my $buffer;
while (<DATA>) {
    $buffer = $1 if /^(john.*)/;
    if ($buffer && /^jacob/) {
        print "$buffer > $_";
        $buffer = '';
    }
}
[download]