Sure it is possible - there are at least two options available:
a) Directory syncronisation (same login data for on-prem & o365)
b) Federated identity (Office 365 authentication occurs with your on-premise AD and there is no re-entering of usernames and Passwords)
Option a) is much easier to setup while option b) is more convenient for users. However, choosing Federated identity comes with high-availablity scenario because if on-premise AD is not available you cannot use any O365 Services because authentication is not possible...)
Further Information can be found at:
Jump Start: Microsoft Office 365 Identity and Access Solutions
www.microsoft.com/.../default.aspx
Blog article
www.centrify.com/.../microsoft_office_365_federated_identity_management.asp
Greetings.
Frank