OWA Certificate Issue

My exchange server is hosted inside the firewall and certificate is isssued from the local certificate server. I am able to acess OWA from inside and outside, but i get an certificate error. The mail server name is mail.company.com and certificate is also issued in same name, but if i try to acess with the same name i wont be able to acess the OWA. If i try to acess it using company.com/exchange i will be able to access it with certificate error. The external dns is hosted with our ISP, do i need to ask my ISP to create a host name or is there any other solution?
If this is not solved i wont be able to use RPC over HTTPS as well.