Steve, I am a hobbyist, not an expert. However, I have a good reference which includes info about the 156th Infantry.
156th Infantry: 25 Nov 40 inducted into federal service at New Orleans LA assigned to the 31st Division and moved to Cp Blanding Fla 22 Dec 40; transferred to Cp Bowie TX 26 Feb 42 where relieved from the 31st Division on 14 July 42; staged at Ft Dix NJ 19 Sep 42 until departed NY 26 Sep 42; arrived in England 6 Oct 42 and 2nd Bn sent to Oran Algeria for military police duties due to its French linguistic ability where it later was redesignated the 202nd Infantry Battalion; regiment assigned to the US Army Assault Training Center at Woolacombe England in July 43 and new 2nd Bn formed from the 3rd Bn, 131st Infantry Regiment; headquarters detachment and Co L assaulted Normandy France on 6 June 44 and entire regiment ashore by 24 June 44; returned to England 6 July 44 and returned to France by echelon 18 Aug-3 Sep 44; guarded flanks of allied advance and Red Ball Express highway; 2nd Bn detached to guard Supreme Headquarters Allied Expeditionary Force headquareters from 15 Oct 44; remainder of regiment moved in mid-Nov 44 to provide security duty at the US Embassy, US Naval Headquarters and other command facilities in Paris; regiment, less 2nd Bn, moved to Normandy coast in mid-Dec 44 where contained German garrisons on the Channel Islands; returned to NY 11 Mar 46 and inactivated at Cp Kilmer NY on 13 Mar 46.
They received campaign credit for: Northern France, Central Europe, Normandy - Co. L, Rhineland - Co. F
You should try to get his personnel record from NPRC. They had a devastating fire in 1973 and many records were lost, but maybe you'll be one of the lucky ones. More info can be found at this web address: http://www.archives.gov/st-louis/index.htmlhttp://www.archives.gov/st-louis/index.html