help understanding public/private keys certs

Hi, we have to communicate with a customer who insist of using secure
communication.
The communication will be done by a SOAP application developed
in .NET, to the customers werbservice.

Now the customer has sent us a public key to connect to their service,
and they have asked us to send
them our public key. So, I went to verisign and ordered a standard SSL
test certificate. I did this
by generating a CSR from IIS6. After giving this on the VeriSign site
I got a certificate with which I
could fininsh the pending request in IIS6.

Now how I see this cert on IIS is that connecting clients can validate
our webserver with VeriSign to see if it is trusted. But how can I
send a public key to our customer. How do I generate this public.
Or is it the same key I have received from VeriSign?

I have tested adding this cert to a webbrowser and connect to the
webserver, but this doen't seem to work.

Just can't grasp this certificate realm, if somone could shed some
light on this matter, please...


Thanks in advance.