Is there a way to serialize an object in such a way that when I retrieve it later it remembers what "type" it was blessed into?

I tried to do this with DBM::Deep, but as you see, no dice.

#test.pl
use warnings;
use strict;
use Data::Dumper;
use DBM::Deep;
use LWP::UserAgent;
use Test::More qw(no_plan);

my $hash = DBM::Deep->new("foo.db");

my $user_agent = LWP::UserAgent->new;
isa_ok($user_agent, 'LWP::UserAgent'); #passes
$hash->{my_user_agent} = $user_agent;
my $user_agent2 = $hash->{my_user_agent}; 
isa_ok($user_agent2, 'LWP::UserAgent');#fails

print Dumper($user_agent2);
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Output of test.pl 2>>test.pl and then test.pl >>test.pl

Failed test (read.pl at line 15)
     The object isn't a 'LWP::UserAgent' it's a 'DBM::Deep'
 Looks like you failed 1 tests of 2.
ok 1 - The object isa LWP::UserAgent
not ok 2 - The object isa LWP::UserAgent
$VAR1 = bless( {
                 'requests_redirectable' => bless( [
                                                     'GET',
                                                     'HEAD'
                                                   ], 'DBM::Deep' ),
                 'max_redirect' => '7',
                 'proxy' => undef,
                 'parse_head' => '1',
                 'use_eval' => '1',
                 'timeout' => '180',
                 'protocols_allowed' => undef,
                 'agent' => 'libwww-perl/5.79',
                 'protocols_forbidden' => undef,
                 'no_proxy' => bless( [], 'DBM::Deep' ),
                 'from' => undef,
                 'max_size' => undef
               }, 'DBM::Deep' );
1..2
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This is sort of a followup to How's mldbm with concurrency?, where I was doing serialization with mldbm. I wound up switching to DBM::Deep on merlyn's advice, but that was before it occurred to me I might be checking for what kind of object I pulled out.

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UPDATE: I think chromatic's Object Serialization Basics is a good place to learn how to do this.