I have done some digging and there are several sources available on the 502nd Infantry. Some collections are spread out and can only be accessed on site, but their finding aids and contact information are listed below.
The National Archives has a number of collections on the 101st and 502nd during WWII, such as regimental histories, general orders, and photograph collections. These can be accessed on the National Archives Catalog (NAC) where finding aids list the content of materials. There is also information on researching veteran records on the NARA website: http://http://www.archives.gov/veterans/
Records of the 502nd Infantry are also located at the US Army Heritage and Education Center in Carlisle, PA. http://http://www.carlisle.army.mil/ahec/index.cfm. The center houses extensive officer and regimental records that can only be accessed on site, but their finding aids are available online. Two collections contain the information I believe you are looking for. The William H. Duncan Papers contains documents consisting of medical papers, maps, references, photographs, operational memos, and a unit roster for the 502nd; this link is a description of the collection. http://https://beta.worldcat.org/archivegrid/collection/data/57562597
The George E. Koskimaki Collection consists of 42 boxes, but it covers a majority of the 101st and its regiments. This is also housed at the US Army Heritage and Education Center. What's interesting about this collection is that Koskimaki interviewed and corresponded with 101st veterans and wrote down their experiences in the war. Extensive Information on regiments (502nd included) are listed in the description: http://https://beta.worldcat.org/archivegrid/collection/data/815732297
Another source location is the Combined Arms Research Library in Ft. Leavenworth, KS. CARL houses an enormous repository of military education records, publications, regimental histories, army unit reports, and first-hand accounts, including a special archival collections section. What's convenient about this facility is that they have made many of their resources available online. Sources on the 101st, 501st, 502nd, and 506th are listed in their collection and can be accessed online through their library website: http://http://usacac.army.mil/organizations/cace/carl
I hope this information helps and good luck on your research!
The Textual Reference Archives II Branch at the National Archives at College Park has custody of World War II unit records among the Records of the Adjutant General’s Office, 1917- (Record Group 407), in the series World War II Operations Reports (Entry 427). The types of records vary by unit, but generally consist of historical reports, “after action” or operations reports, unit journals, and general orders. We do not have a name index to the records. The files do not include personnel or medical information and they typically include very little to no information relating to individual servicemen, so they are highly unlikely to contain detailed information about your father's service. However, depending on the unit, the records occasionally include casualty lists that list "wounded in action." The unit records would prove more useful in providing information about the unit's involvement in a particular battle.
If you would like more information about World War II unit records, you may e-mail email@example.com. Be sure to include the specific unit (i.e., division, regiment, battalion) and date(s) of interest, which are necessary for the reference archivists to conduct a search.
For a more concise, narrative overview of the battle, you may also wish to consult the Army's official history of World War II (commonly referred to as the "Green Books"), which is available to view or download on the U.S. Army Center of Military History website. The Normandy operations appear to be primarily covered in the volume, "Cross Channel Attack - U.S. Army Center of Military History."
Best of luck in your research!