Ta dah! I know that strictly speaking, you're not supposed to do complicated things like parsing XML yourself, but I couldn't resist:

use Data::Dumper;
use strict;

my ($xml, $account, $asset, @record);

$xml = parseXML(join '', <DATA>);
print Dumper($xml);

for $account (@{$xml->{'account'}}) {
    $account->{'asset'} = [$account->{'asset'}]
        if !ref $account->{'asset'};
    for $asset (@{$account->{'asset'}}) {
        @record = ($account->{'accountId'}, $account->{'accountName'},
+ $asset->{'assetId'}, $asset->{'assetName'});
        print "@record\n";
    }
}

sub parseXML {
    my $xml = $_[0];
    my (%xml, $key, $val);

    while ($xml =~ m|<(.*?)>(.*?)</\1>|sg) {
        ($key, $val) = ($1, $2);
        if (!defined $xml{$key}) {
            $xml{$key} = parseXML($val);
            next;
        }
        $xml{$key} = [$xml{$key}] if ref $xml{$key} ne 'ARRAY';
        push @{$xml{$key}}, parseXML($val);
    }
    return scalar keys %xml == 0 ? $xml : \%xml;
}

__DATA__
<xml version, encoding & SOAP Envelope header stuff...>
<account>
    <accountId>001</accountId>
    <accountName>Account 001</accountName>
    <asset>    
        <assetId>abcd</assetId>
        <assetName>Asset abcd</assetName>
    </asset>
    <asset>
        <assetId>wxyz</assetId>
        <assetName>Asset wxyz</assetName>
    </asset>
</account>
<account>
    <accountId>002</accountId>
    <accountName>Account 002</accountName>
</account>
</SOAP Envelope stuff...>
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