Hi Christiaan,
Thanks for visiting Apple Support Communities.
You can send Calendar invitations with other email addresses if your email provider supports it, for example, Yahoo, Gmail or an Exchange account.
If your email provider supports it, here's how to add the account to Calendar:
Add calendars from other services
You can also add appointments from other popular services to your calendar in Calendar app, including Exchange, CalDAV, Facebook, and Yahoo.
- Choose Apple Menu () > System Preferences.
- Select Internet Accounts.
- Click the Add Account ➕ button at the bottom of the window.
- Choose the account type you want to use, and enter your account credentials.
- Make sure the option "Calendars" is selected (checked) to display the events associated with this account in the Calendar app.
You can find this information here:
Mac Basics: Calendar keeps your appointments
http://support.apple.com/kb/HT5978
Regards,
Jeremy