In a heterogeneous overlay wireless network, a mobile node (MN) with multiple wireless interfaces can attach to various networks and obtains multiple IP addresses simultaneously. To allow correspondent nodes (CNs) to connect to an MN at anytime through any MN's IP address, an MN must keep its interfaces awake to receive incoming packets. Unfortunately, the previous studies indicate that power consumption of an MN with multiple interfaces poses a serious problem, even when interfaces are idle. This work presents two novel energy-conserving always-on schemes for an MN with multiple interfaces. These schemes only maintain one awake interface of an MN and turn off completely other interfaces of the MN to minimize its power consumption. By updating proper binding information on home agents (HAs), packets sent to the IP addresses associated with these turned-off interfaces can be received by the MN without packet loss.