I wondered how this might be achieved so decided to have a go. I prepared a ZIP archive containing three bzip2'ed files (man page outputs) stored without further compression.

$ man ls > ls.man
$ man xterm > xterm.man
$ man cp > cp.man
$ bzip2 -v *.man
  cp.man:     2.496:1,  3.206 bits/byte, 59.93% saved, 5690 in, 2280 o
+ut.
  ls.man:     2.644:1,  3.026 bits/byte, 62.18% saved, 8093 in, 3061 o
+ut.
  xterm.man:  5.062:1,  1.580 bits/byte, 80.24% saved, 264279 in, 5221
+0 out.
$ zip -0m mans *.man.bz2
  adding: cp.man.bz2 (stored 0%)
  adding: ls.man.bz2 (stored 0%)
  adding: xterm.man.bz2 (stored 0%)
$
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The following script constructs an Archive::Zip object to access the ZIP file and gets a list of member files. Then for each member it creates a member object and uses that to obtain the content. A reference to this content, by way of an on-the-fly subroutine, is used as the argument to the IO::Uncompress::Bunzip2 constructor which can then be read line by line. I just print the first five lines of each member file to demonstrate that the method works. I have not incorporated any error checking, this is left as an exercise for the reader.

use strict;
use warnings;

use 5.014;

use Archive::Zip;
use IO::Uncompress::Bunzip2;

my $zipFile = q{mans.zip};
my $zip     = Archive::Zip->new( $zipFile );
my @members = $zip->memberNames();

foreach my $member ( @members )
{
    say qq{Member: $member};

    my $memberFH = $zip->memberNamed( $member );
    my $bzFH     = IO::Uncompress::Bunzip2->new(
       sub { \ $_[ 0 ] }->( $memberFH->contents() )
       );

    my $lineCt   = 0;
    while ( my $line = $bzFH->getline() )
    {
        last if $lineCt ++ > 5;
        print $line;
    }
}
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The output.

Member: cp.man.bz2
CP(1)                                        User Commands            
+                            CP(1)



NAME
       cp - copy files and directories
Member: ls.man.bz2
LS(1)                                        User Commands            
+                            LS(1)



NAME
       ls - list directory contents
Member: xterm.man.bz2
XTERM(1)                                    X Window System           
+                         XTERM(1)



NAME
       xterm - terminal emulator for X
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I hope this is useful.