> openssl s_client takes host names, not URLs. Try
> openssl s_client -connect www.domain.com:443

yep, you'right.

[]# openssl s_client -connect www.domain.com:443 -cert ssl.crt -key ssl.key

Error message:
---------
CONNECTED(00000003)
depth=0 /C=US/ST=California/L=San Francisco/O=My Company/OU=IT/CN=www.domain.com
verify error:num=20:unable to get local issuer certificate
verify return:1
depth=0 /C=US/ST=California/L=San Francisco/O=My Company/OU=IT/CN=www.domain.com
verify error:num=27:certificate not trusted
verify return:1
depth=0 /C=US/ST=California/L=San Francisco/O=My Company/OU=IT/CN=www.domain.com
verify error:num=21:unable to verify the first certificate
verify return:1

---
Certificate chain
0 s:/C=US/ST=California/L=San Francisco/O=My Company/OU=IT/CN=www.domain.com
   i:/C=US/O=Security Firm/CN=Security CA-1
---
...
---
No client certificate CA names sent
---
SSL handshake has read 944 bytes and written 324 bytes
---
New, TLSv1/SSLv3, Cipher is RC4-MD5
Server public key is 1024 bit
SSL-Session:
    Protocol  : TLSv1
    Cipher    : RC4-MD5
    Session-ID: B504440030B7B50633ECD7FED781458B190213F63EA0B5B8A966615B98E6F2AA
    Session-ID-ctx:
    Master-Key:
3BB9246CF8456FF525E4695X4440017FB3B00CB29493BB5A2BTBF80EBAFB7A59599CF9A5497C599AB8FF9FAAD8390A0B
    Key-Arg   : None
    Krb5 Principal: None
    Start Time: 1201080084
    Timeout   : 300 (sec)
    Verify return code: 21 (unable to verify the first certificate)