Utility Grids implement a virtualization architecture and allow for sharing of infrastructure for improved return on investment (ROI). We consider extending the existing Grid infrastructure to support interactive sessions in an enterprise setting. This would allow users to remotely execute interactive applications in the Grid and view their output using remote display technologies. We propose a resource allocation architecture to support such interactive sessions in utility Grids. End-users submit requests for a remote desktop session. A utility Grid site resource allocation system assigns a compute node for this request considering performance needs of such remote desktop sessions. We also propose a hierarchical admission control system. The system consists of a site admission control system for admission control of remote desktop sessions, and a session admission control system at the compute node for admission check of per-application interactive sessions. We also present discussion on mixed workloads consisting of requests for batch jobs and interactive remote desktop sessions.