As businesses are increasingly relying on the cloud to host their services, cloud providers are striving to offer guaranteed and highly-available resources. To achieve this goal, recent proposals have advocated to offer both computing and networking resources in the form of Virtual Data Centers (VDCs). Subsequently, several attempts have been made to improve the availability of VDCs through reliability-aware resource allocation schemes and redundancy provisioning techniques. However, the research to date has not considered the heterogeneity of the underlying physical components. Specifically, it does not consider recent findings showing that failure rates and availability of data center equipments can vary significantly depending on various parameters including their types and ages. To address this limitation, in this paper we propose a High-availability Virtual Infrastructure management framework (Hi-VI) that takes into account the heterogeneity of cloud data center equipments to dynamically provision backup resources in order to ensure required VDC availability. Specifically, we propose a technique to compute the availability of a VDC that considers both (1) the heterogeneity of data center networking and computing equipments in terms of failure rates and availability, and (2) the number of redundant virtual nodes and links provisioned as backups. We then leverage this technique to propose an allocation scheme that jointly provisions resources for VDCs and backups of virtual components with the goal of achieving the required VDC availability while minimizing energy costs. Through simulations, we demonstrate the effectiveness of our framework compared to heterogeneity-oblivious solutions.