I have a little more time now so I figured I might as well show how I would alter your schema to work with Class::DBI (I am not claiming this is the way you should do it, merely how I would):

package My::User;

use base 'My::ClassDBI';

__PACKAGE__->table ('user');
__PACKAGE__->columns ( All => qw( uid name login ) );
__PACKAGE__->has_many( 'capabilities', 'My::UserCapability' => 'user' 
+);

###

package My::Capability;

use base 'My::ClassDBI';

__PACKAGE__->table ('capability');
__PACKAGE__->columns ( All => qw( capid name default ) );
__PACKAGE__->has_many( 'users', 'My::UserCapability' => 'capability' )
+;

###

package My::UserCapability;

use base 'My::ClassDBI';

__PACKAGE__->table ('user_capability');
# note the added primary key idx
__PACKAGE__->columns ( All => qw( idx user capability ) );
__PACKAGE__->has_a( 'user' => 'My::User' );
__PACKAGE__->has_a( 'capability' => 'My::Capability' );
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You could now print out all the capabilities for a user with:

foreach ( $user->capabilities() ) {
    print $_->capability->name(), "\n";
}
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or all the users with a certain capability:

foreach ( $capability->users() ) {
    print $_->user->name(), "\n";
}
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The users and capabilities methods might be better named as they don't really return a list of users or capabilites but rather return a list of My::UserCapability objects. But you could write a custom get_capabilities method such as:

sub get_capabilities {
    my ( $self ) = @_;

    my @capabilities = $self->capabilities();

    return map { $_->capability->name() } @capabilities;
}
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It is a bit of work getting around the single primary key limitation of Class::DBI but IMHO well worth it.

NOTE: I think all the code is correct as given but I could be drastically wrong as it is late on a Friday afternoon.