The above appears to fill the bill. The regiment was activated as 533d Engineer (Shore) Regiment at Camp Edwards, Massachusetts in August 1942 and redesignated 533d Engineer (Amphibian) Regiment three months later. Underwent amphibious training at Camp Carabelle, Florida, November1942 to April 1943. Arrived Fort Ord, California 27 April 1943. Redesignated 533d Engineer (Boat & Shore) Regiment May 1943. Staged at Camp Stonemen, California 2-22 December 1943 and departed San Francisco for duty in the Pacific Theater 22 December 1943. Arrived Goodenough Island 12 January 1944. Cape Gloucester, New Britain, Solomon Islands 20 February 1944. Finschhafen, New Guinea 26 June 1944 (assigned to 2d Engineer [Special] Brigade). Participated in the assault landings at Lingayen Gulf, Leyte, Philippines 9 January 1945 and arrived at Malabang, Mindanao, Philippines, 17 April 1945. Inactivated December 1945 in the Philippines. Decorations: none. Campaign participation credits: Bismarck Archipelago, Luzon (Invasion), Luzon (campaign), Southern Philippines. How any of the above applies to your Dad depends on his dates of service with the regiment. You would have to access records to determine service with commando unit and service in Italy and Germany.
The Army Engineer Association has a website at < http://www.armyengineer.com/http://www.armyengineer.com/ > (click on the address to go there). They may be able to assist in securing more information, locating comrades, etc. You can contact them via e-mail from the website.