A control-plane component of a virtual network interface (VNI) multiplexing service assigns one or more VNIs as members of a first interface group. A first VNI of the interface group is attached to a first compute instance. Network traffic directed to a particular endpoint address associated with the first interface group is to be distributed among members of the first interface group by client-side components of the service. The control-plane component propagates membership metadata of the first interface group to the client-side components. In response to a detection of an unhealthy state of the first compute instance, the first VNI is attached to a different compute instance by the control-plane component.