Cloud computing has become a cost-effective model for deploying online services in recent years. To improve the Quality-of-Service (QoS) of the provisioned services, recently a number of proposals have advocated to provision both guaranteed server and network resources in the form of Virtual Data Centers (VDCs). However, existing VDC scheduling algorithms have not fully considered the reliability aspect of the allocations in terms of (1) hardware failure characteristics on which the service is hosted, and (2) the impact of individual failures on service availability, given the dependencies among the virtual components. To address this limitation, in this paper we present a technique for computing VDC availability that considers heterogeneous hardware failure rates and dependencies among virtual components. We then propose Venice, an availability-aware VDC embedding framework for achieving high VDC availability and low operational costs. Experiments show Venice can significantly improve VDC availability while achieving higher income compared to availability-oblivious solutions.