First off, take a moment to get all of those Army/Navy rivalry jokes out of your system. We'll wait.
The storied history of the US Army and US Navy partnership is as old as the branches themselves. Working together, this interbranch cooperation comes in three different forms: Supplies, Transport, and Direct Support.
Here's what The_Chieftain has to say about the three:
This one is the most visible.
The thought process of a solider requisitioning new supplies during the Second World War generally extended as far as figuring out which forms to fill out, where to submit them, and how long it would take for the supplies to arrive. He probably didn't spare much thought to the matter of how the supplies actually got to where he could pick them up: They showed up on the back of a deuce-and-a-half and that was good enough for him.
He probably didn't spare much thought for the lookout getting hammered on a Canadian corvette in a North Atlantic storm escorting a convoy through the U-boat hunting grounds, or the merchant mariners who found themselves swimming for their lives in the hostile waters after a German eel struck its target. Just as likely, the Canadian sailor wasn’t thinking much about the soldier shivering in his foxhole after days of unconscionable snow with no source of heat. They all had problems of their own to deal with, even though the soldier was the reason that the sailor was in the North Atlantic in the first place. Without supplies, the soldier is unarmed. Without the soldier to supply, the merchant sailor has no role. The partnership is imperative, if not obvious.
The transport side of things is a bit easier to understand: the soldiers themselves were often at the hospitality of their naval colleagues. This usually took the form of an opposed landing. Although such things are normally considered the purview of the Marines, the Army conducted more landings during the Second World War than the Marines did.
Even early successes could have been a bit rocky: The Army’s landing in North Africa as part of Operation Torch was both a triumph for the Navy, as well as a very sharp pain point on lessons learned as part of the first long-distance landing operation the Navy conducted. This sort of thing wasn’t confined just to just the Second World War, of course: Half the forces landing at Inch’on in Korea were Army, and even in the Persian Gulf and Grenada conflicts, the Army was conducting flight operations off Navy ships. Schwartzkopf’s book relates an incident where in the middle of the Grenada operation, the Pentagon told the Navy not to refuel Army helicopters as they hadn’t figured out the budget process yet. He ignored it.
Direct support is exactly what it sounds like: naval personnel or vessels providing direct combat support to Army land operations. The river Patrol Boats such as in Vietnam, or the Brown-Water Navy, were right in the thick of things on the two-way firing range. More common, though, is fire support, either air or gunfire. Not that there’s anything wrong with a battery of Army 105mm on the other end of the radio, but when there’s a battleship ship with nine 16-inch rifles, or a modern cruiser with two 5” guns each firing off a round every three seconds, that puts the possible boom into perspective. And of course, that’s not counting the possibilities from aircraft carriers.
The Navy also sends folks ashore, such as Seabees. When I was in Afghanistan, I encountered sailors of all stripes, from corpsmen to SSBN commanders, particularly in the Provincial Reconstruction Teams which mixed Army personnel with others. We wore the same camouflage, but where we would wear a unit patch, the Navy personnel would wear a Navy Jack.
So, to the lads and lasses who are Not Army Verified Yet, a tip of that hat, and let us continue on this cooperative tradition into the next century!