Can i use CA signed cert to create client authentication certificates ?

I am trying to set up apache with mod_ssl , and I have it working with a
Self Signed CA.
But i can not get it to work with a cert created by thawte.com.

Does anyone know if it is possible to do this with a crt signed by a "third"
party where one does not have access to their root ca key ?.

Ie.

I have generated a : apache_server.key made a apache_server.csr and sent
this for signing by thawte.com
Recived a apache_server.crt

Created a client.key and a client.csr
Signed it with my apache_server.key and apache_server.crt

Converted the client.key,crt to a pkcs12 file and imported this into my
browser but i can not make things work.

SSL works fine on the server on pages that does not require SSL client auth.

A I stated earlier, IT works when I create and self sign a CA, but I cant
make it work when I use a 3rd party CA and only have apache_server.key,
apache_server.crt , thawte root cert.

Best regards

Wizkidnono
–œ…â'µêßiÇ­ ê^$‹š‡l²\0Âj²Éh®,z´®¦š+´Æ¢–)à.+-š‡l²[¬z»&¡Û,–Šàëh™«^t¸¬´Æ§j«™¨è­Ú&¢j²Éh®