Using battery and USB power at the same time
In the case of the application note, you could replace Q1 with another diode, then the load would draw power from which ever source has the higher voltage, or from both if they are at approximately the same voltage.  But note that this circuit doesn't provide 5V output or any voltage regulation for that matter.  If nothing is plugged in you would get the battery voltage (~4V), if USB is plugged in you would get about 5V, and if the AC adapter is plugged in you would get whatever voltage that provides (minus the diode voltage drops).

You mentioned charging, and 5V output, so you might need a separate charger IC, as well as a boost regulator (assuming you use one LiPo cell) to get the 5V output.  There are some devices that have such capabilities combined, such as the LTC4090 device.  It will take a battery, USB input, and even another high voltage input, charge the battery, and give a 5V output (in the case of the LTC4090-5 device).