Okay, that complicates things a little, but this seems to work:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

sub dhm2int {
    my( $d, $h, $m ) = unpack '(A2)*', $_[0];
    return ( ( $d - 1 ) * 24 + $h ) * 60 + $m;
}

sub int2dhm {
    sprintf "%02d%02d%02d", int($_[0]/1440)+1, int($_[0]/60)%24, $_[0]
+%60;
}

sub adjacentPairs (&@) {
    my $code = shift;
    map {
        $code->( shift(), $_[0] );
    } 1 .. @_;
}

#my @listone = 
#    (['010000','010010',2],['010200','010210',5],['012359','020001',3
+]);
#my @listtwo = 
#    (['010005','010015',1],['010207','010211',4]);
my @listone = 
    (['010000','010110',6],['010200','010210',5],['012350','020012',3]
+);
my @listtwo = 
    (['010005','010015',1],['010207','010211',4],['012355','020003',1]
+);

my @res = adjacentPairs{
    defined( $_[1] ) ? do {
        $_[1][3] > $_[0][3]
            ? [ $_[0][0], int2dhm( $_[1][3] - 1 ), $_[0][2] ]
            : [ int2dhm( $_[1][4] + 1 ), $_[0][1], $_[0][2] ]
    }
    : [ @{ $_[0] }[ 0 .. 2 ] ]
} sort {
    $a->[ 3 ] <=> $b->[ 3 ]
    ||
    $b->[ 4 ] <=> $a->[ 4 ]
} map {
    my $in = $_;
    my $s = dhm2int( $in->[ 0 ] );
    my $e = dhm2int( $in->[ 1 ] );
    my @out;
    while( int( $s / 1440 ) != int( $e / 1440 ) ) {
        my $newe = ( int( $s / 1440 ) +1 ) * 1440 -1;
        push @out, [ int2dhm( $s ), int2dhm( $newe ), $in->[2], $s, $n
+ewe ];
        $s = $newe +1;
    }
    ( @out, [ int2dhm( $s ), $in->[1], $in->[2], $s, $e ] );
} @listone, @listtwo;

pp \@res;

__END__
c:\test>junk33
[
  ["010000", "010004", 2],
  ["010005", "010015", 1],
  ["010200", "010206", 5],
  ["010207", "010211", 4],
  ["012359", "012359", 3],
  ["020000", "020001", 3],
]

c:\test>junk33
[
  ["010000", "010004", 6],
  ["010005", "010159", 1],
  ["010200", "010206", 5],
  ["010207", "012349", 4],
  ["012350", "012354", 3],
  ["012355", "012359", 1],
  ["020004", "020012", 3],
  ["020000", "020003", 1],
]
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Note: The second set of results apply to the second (uncommented) set of data

One consequence is that the output is not longer in strictly sorted order. If this is a requirement a second sort will be required.