use strict;

my @filenames = qw/one.txt two.txt three.txt/;
my @filehandles;

foreach my $filename (@filenames) {
    open my $fh, '<', $filename or die "Could not open $filename; $!";
    push @filehandles, $fh;
} ## end foreach my $filename (@filenames)

while (1) {
    my $lines_ref = read_lines_parallel(@filehandles);
    last unless $lines_ref;
    print join '|', @$lines_ref;
    print '-' x 20, "\n";
} ## end while (1)

sub read_lines_parallel {
    my @filehandles = @_;
    my @lines;
    foreach (@filehandles) {
        push @lines, scalar <$_>;
    } ## end foreach (@filehandles)
    if ( join '', @lines ) {
        return \@lines;
    } ## end if ( join '', @lines )
    else {
        return undef;
    } ## end else [ if ( join '', @lines )
} ## end sub read_lines_parallel


##</code><code>##

first line file 1
|line 1 file 2
|first line file 3
--------------------
second line file 1
|line 2 file 2
|second line file 3
--------------------
third line file 1
||third line file 3
--------------------
||fourth line file 3
--------------------
##</code><code>##

while (1) {
    my $lines_ref = read_lines_parallel(@filehandles);
    last unless $lines_ref;
    print join '|', @$lines_ref;
    print '-' x 20, "\n";
}
##</code><code>##

while (my $lines_ref = read_lines_parallel(@filehandles)) {
    # Do something with $lines_ref or @$lines_ref here
    print join '|', @$lines_ref;
    print '-' x 20, "\n";
}