The entire effort is to gain experience working together. Most military ventures these days are multi-national efforts. The bombing of Libya for example, was a combination of many air forces were working together. No country donates a lot of military forces (less money) but, as a combined force it is far stronger than what Libya could deal with. While the US said no US aircraft flew into Libyan air space. The USA contributed EA-18Gs, the E-2C and, many tomahawk missiles were used first. Other countries contributed land attack missiles. The Rafale and Typhoon saw their first combat.
Well, I was thinking in terms of cross-decking, cross-crewing but with a view also (perhaps in future) towards one nation providing one capability and the other another, complementary capability (e.g. heli’s <> LHD). In the event a nation can no longer afford to acquire or maintain both capabilities.