We want to have a single SSL certificate for a web site so that the website can be accessed with a domain name and IP address. Is this possible?
Yup, when the
SAN field of the SSL certificate contains the
IP:XXX.XX.XX.XXX value it's possible to successfully connect to such a service without warnings (for a known CA, of course).
But in reality this has to be supported by the CA you are buying the certificate from. In my experience I don't remember seeing such options in commercial CA web interfaces, though this doesn't mean you won't find one.