Communication networks are embracing the software defined networking (SDN) paradigm. Its architectural shift assumes that a remote SDN controller (SDNC) in the control plane is responsible for configuring the underlying devices of the forwarding plane. In order to support flexibility-motivated network slicing, SDN-based networks employ another entity in the control plane, a network hypervisor (NH). This paper first discusses different protection strategies for the control plane with NHs and presents the corresponding availability models, which assume possible failures of links and nodes in the forwarding plane and the control plane. An analysis of these protection alternatives is then performed so as to compare average control plane availability, average path length for the control communication that traverses NH, and infrastructure resources required to support them. Our results confirm the intuition that the NH introduction generally results in a reduction of the control plane availability, which stresses the need for appropriate protection. However, the availability achieved by each of the considered strategies is impacted differently by the node availability and the link failure probability, thus calling for a careful selection that is based on the infrastructure features.