From a Parent you can fire a 'RefreshRequested' into a contained mashup.
There isn't a direct way to do the same from a contained mashup to the parent, so a workaround needs to be used. Either use a mashup parameter that exists in both the Parent and Contained mashup and you connect those together. Then when you set the value in the Contained mashup, you can use the MashupParameterValueChanged Event in the parent to trigger something. Or do something similar but with Session Parameters, not sure if that works though (never had to try)
If you use PopUps, there is a 'OnPopUp Closed' Event that you can use, but that doesn't look like it will apply to what you are trying to do.