Maybe something like this?

open my $func1, "|-", q{perl -ne 'print "function1 (PID $$): processin
+g $_"; sleep 1'};
open my $func2, "|-", q{perl -ne 'print "function2 (PID $$): processin
+g $_"; sleep 3'};
use IO::Handle;
$func1->autoflush();
$func2->autoflush();

while (my $record = <DATA>) {
    print $func1 $record;
    print $func2 $record;
}

__DATA__
foo
bar
baz
[download]

Output:

$ ./840957.pl
function1 (PID 21667): processing foo
function2 (PID 21668): processing foo
function1 (PID 21667): processing bar
function1 (PID 21667): processing baz
function2 (PID 21668): processing bar
function2 (PID 21668): processing baz
[download]