A networking manager of an extension server of a virtualized computing service detects that a data link layer frame has been obtained at the extension server. The networking manager delivers at least a portion of contents of the frame to a compute instance running at the extension server in response to determining that a destination media access control (MAC) address of the frame matches a MAC address of a local-premise-access virtual network interface attached to the compute instance. The local-premise-access virtual network interface is not assigned an Internet Protocol (IP) address from a range of IP addresses managed by the virtualized computing service.