You can create separate CNAME (alias or canonical name) records for subdomains to point to Office 365 servers or Google servers alike. gmail.yourdomain.com and outlook.yourdomain.com could co-exist and point to both services. But, as you can tell from my example domains, both services are similar and using both at the same time would be unusual.
Office 365 is Microsoft's competitive solution to Google Apps.
Google apps has it's own web applications for creating and editing documents, spreadsheets, preasentations, forms, databases, and drawings. It's had it for years.
Microsoft office has traditionally been software you purchase a licence to use, and then install it on a computer or device you plan to access it on. It still is, but Microsoft is making a huge move to the cloud. In doing so, with Office 365, your documents will be on their servers -much like google apps -complete with collaboration ability. Office 365 is a subscription service costing $6 per user per year. Google apps is free on a domain with 10 or fewer users or $50 Per user per year (4.16 per used per month) and there's nothing to install.
Using both services side by side is redundant. Pick one.
Or, if you like Google Apps, but you're in a position where you need to continue using Microsoft Office, you can easily have both by storing your office documents in Google Docs. Drag and drop them into your doc list to upload.
Can you host a domain with Google Apps and use it for Office 365?
