The following should get you started:

use warnings;
use strict;

my %bills;
my $currBill = 'void';
my $type = 'header';

while (<DATA>) {
  chomp;
  if (/^1010100\.+(\d+)/) {
    $currBill = $1;
    $type = 'header';
  } elsif (/^3010330\.+(\d+)/) {
    $currBill = $1;
    $type = 'data';
  } else {
    push @{$bills{$currBill}{$type}}, $_;
  }
}

for my $bill (sort keys %bills) {
    print ">>>> $bill\n";
    print "Header\n" . (join "\n", @{$bills{$bill}{'header'}}) . "\n"
        if exists $bills{$bill}{'header'};
    print "Data\n" . (join "\n", @{$bills{$bill}{'data'}}) . "\n"
        if exists $bills{$bill}{'data'};
}

__DATA__
1010100.........123456.....   #header line for bill # 123456
#some data
#some data
#some data
#some data
1010100.........678910.....    #header line for  bill # 678910
#some data
#some data
#some data
3010330.........123456.....   #bill detail for bill 123456
#some data
#some data
#some data
#some data
#some data
3010330.........678910.....   #bill detail for bill 678910
data for 678910
[download]

>>>> 123456
Header
#some data
#some data
#some data
#some data
Data
#some data
#some data
#some data
#some data
#some data
>>>> 678910
Header
#some data
#some data
#some data
Data
data for 678910
[download]

Open your files in the for loop, print their contents as required and then close.