The USCG was very much an equal partner for Operation NEPTUNE, the naval portion of the Normandy Landings. They manned larger attack transports, and landing craft, and were present at all 5 beaches. Often they would also simply provide additional manpower for Navy ships, but many sailed with all Coastie crews. In particular with so many boat crews needed by the Navy in the Pacific, a significant number of landing craft of all sizes that actually put the men on the beach were manned by Coast Guardsman.

At the urging of FDR several dozen small cutters were also sent to Europe to serve as rescue craft in the Channel both for downed airmen, and shipwrecked men from the invasion fleet. While others served as escorts and guides for the small landing craft as they made their way from England and assembled to head to the beach after loading on the assault troops.

As for the American homeland. The Coast Guard was big enough for both, along with the USN. Dozens of cutters and aircraft from both services patrolled the coasts, escorted convoys and hunted subs. While the USCG alone operated nearly 150 combatant craft, several hundred more smaller cutters, and hundreds of transports of all kinds had crews aboard. Backed by Navy units, nd hunter killer forces built around carriers to hunt the subs actively, and long raged patrol aircraft based ashore. While the RN and RCN contributed mightily as well.

The USCG was present then everywhere the Navy was, and this is not an isolated event. They operated in Vietnam, and continue to do so today in the Persian Gulf.

For more here is the Coast Guard's official history of its participation at Normandy: https://www.uscg.mil/history/articles/h_normandy.asp

And, logically I guess, who was guarding the US coast while I was in Europe?