Whenever I connect to "http://localhost:20010" I get the proper https repsonse from server "https://sslwebsite.xxxx.com". 

But the moment I add, "https://localhost:20010/someprogrampath", I get "404 File Not found error". But if I access, "https://sslwebsite.xxxx.com/someprogrampath" directly it WORKS.

Any ideas?

I use the following configuration. 
===================================
; Authentication stuff
verify = 2
; Don't forget to c_rehash CApath
;CApath = c:\certs
; It's often easier to use CAfile
CAfile = c:\certs\MetavanteTest_client.pem
; Don't forget to c_rehash CRLpath
;CRLpath = crls
; Alternatively you can use CRLfile
;CRLfile = crls.pem

; Some debugging stuff useful for troubleshooting
debug = 7
output = c:\stunnel.log

; Use it for client mode
client = yes

; Service-level configuration

;[pop3s]
;accept  = 995
;connect = 110

;[imaps]
;accept  = 993
;connect = 143

;[ssmtp]
;accept  = 465
;connect = 25

[https]
cert = c:\certs\xxxx_client.pem
accept  = 20010
connect = sswebsite.xxxx.com:443
;TIMEOUTclose = 0
; vim:ft=dosini

sslVersion = all
=========================================