When you host your company website on Microsoft SharePoint Online, as an administrator, you can choose to change the site to use a vanity domain name instead of continuing to use the domain you chose when you signed up for Microsoft Office 365 for professionals and small businesses: for example, contoso.sharepoint.com. Changing the domain name for your public site enables customers to access your site by using an existing domain name that you own, or a new domain name that you’ve chosen and purchased for your business.
To use your vanity domain with Office 365, you first add your company’s registered domain name to the service. For more information, see Add and verify a domain. After you’ve added your domain, you can configure Office 365 to use the domain name for your public Office 365 website. For more information about setting up a website on SharePoint Online, see Set up a public Website.
You can host one website with your Office 365 account, and you can point only one domain to the website. Also be aware that you cannot use Secure Sockets Layer (SSL) protocol with an Office 365 hosted site.
After you configure Office 365 to use your vanity domain for your website, you can easily change the site to use another vanity domain name or change back to the original domain name that you used (for example, contoso.sharepoint.com), by following the steps provided in this topic. Or you can, if you like, choose at a later time to move the site to be hosted by another third-party service.
To configure Office 365 to use a vanity domain for your public website, follow these steps.
On the Admin page, in the left pane, under Management, click Domains.
Click Change address, and then step through the wizard.
Why SSL can not be used to access Office 365 sites?
And what is the alternative to this typical secure access method then?
For normal Office 365 sharepoint sites , ssl is by default .... but this informatio is true only for the public facing site which is a new option in office 365
Understanding the details of how the two subscription types work with custom domains can help you choose the right subscription for your needs, and help you add and manage your domain more easily in Office 365.
For example, consider the following differences:
•Both subscriptions allow you to continue to host your current website outside of Office 365, but with a “P” subscription, you’ll need to take a few additional steps to get this working correctly.
•With a “P” subscription, you’ll manage DNS records in Office 365 after adding your domain, while with an “E” subscription, you continue to manage the records with your current DNS hoster.
•With a “P” subscription, you can add second-level domains, such as contoso.com but you cannot add subdomains, such as partners.contoso.com. With an “E” subscription, you can have multiple subdomains: for example, www.contoso.com, www.partners.contoso.com, www.partners.marketing.contoso.com, and so on.
When will it be available? Have dozens of customer to migrate, but we need HTTPS on custom domain names.
Very nice article about public facing sites.
I'm working with branding for the public facing sites, let me introduce our work, take a look at http://bindtuning.com/
We have a tuning tool where you can fully customize a theme for SharePoint and besides being responsive the theme include a lot of features.