I did now your test, seems that it was my fault - something wrong with my secur key:
/usr/local/sbin/lighttpd -f /var/etc/lighty-webConfigurator.conf
firewall:~# /usr/local/sbin/lighttpd -f /var/etc/lighty-webConfigurator.conf
2008-03-28 16:25:26: (network.c.377) SSL: Private key does not match the certificate public key, reason: error:140A80B1:SSL routines:SSL_CTX_check_private_key:no certificate assigned /var/etc/cert.pem
firewall:~#
I generatet a new set key and certificate, now https workes with my certificate.