For a USB/battery-powered project at work we're using the TI
bq24072. It does exactly what you seem to need: when a charger is connected, it charges the battery and powers the rest of the system from the charger, and if you disconnect the charger, it switches to the battery. This happens without interruption (or at least fast enough that the system doesn't seem to notice.)
A similar chip is the
MCP73871. The keyword with both is
autonomous power source selection.
They're both bigger devices than the one you mentioned, but they're not as complex as they seem at first glance; you probably don't need all their pins and can simply tie some to VDD or GND, and you'll save the hardware you'd otherwise need for switching between sources.