Almost ZIP .... IME USN does not typically work anywhere near the US. Exception while I was still active (retired 10 years now) was Maritime Counter Drug work. For a long time USN surface assets (ships) were assigned to patrol for drugs both in the Carib and in the Pacific. No task forces ... but a ship or two allowed to play independently for a while ... WHILE hosting an embarked USCG LEDET (law enforcement detachment). If the USN ship spotted a suspect they'd run up the CG Ensign and technically the LEDET OIC became the On Scene Commander. Control of the USN vessel would "CHOP" (change operational commander) to USCG, and the 'drug mission' pursued; and technically the CG OIC, usually an O-2 was telling the NAVY CO, an O-5 what to do ..... Because as you know the MILITARY can not perform law enforcement under normal circumstances while USCG, altho a military branch, has as a primary mission of LAW ENFORCEMENT.
Also, when in command of a HIGH ENDURANCE CUTTER in the Pacific we refueled at sea from NAVY tankers routinely .... but only the largest CG Cutters have this capability: to use a NAVY fueler. Our 210 foot medium 'ships' couldn't hold up the big hoses!!!!!
Another exception might be the Sub Base at say Kings Bay. But here the interaction is reverse from what you suggest. USN has funded an upgraded CG presence here to provide an enhanced 'law enforcement' component to "vessels" transiting to/from Kings Bay. Once again .... a question of USCG legal authority versus NAVY/DOD in a non 'military' posture.