All medical personnel were officially assigned to medical detachments, one in each regiment. From there combat medics were detailed to combat units where they participated in operations. Some were with these units for long periods of time whereas others were moved around frequently as needed.
The operation you referred to was the battle of Lindern, Germany, which commenced in the early morning hours of November 29th, 1944. The operation was primarily led by the 3rd Battalion of the 335th Infantry but on that day and those following there were many other elements of the Division involved. Without further information and very diligent research it is not possible, if ever, to determine the unit in which Jerome Miller was working when he was fatally wounded.
Lindern, on higher ground above he Roer River, was the crucial place that it was necessary to take and hold in order to enable the eventual crossing of the Roer and the route to the Rhine. On November 29 I was with Company K, 335th Infantry, which together with Company I led the initial early-morning attack. The battle that proceeded over the next few days is described in detail in pages 185-244 of my memoir "Dear Captain, et al.: the Agonies and the Ecstasies of War and Memory." That book is available in a variety of formats through most Internet booksellers. One example is at Amazon as noted here: https://www.amazon.com/Dear-Captain-al-Agonies-Ecstasies/dp/0738818550/ref=asap_bc?ie=UTF8
Many thanks for your inquiry and if you have further questions I would be glad to try and answer them.
This board is dedicated to the memory of CAPTAIN LEONARD REED CARPENTER, Company Commander, November 19, 1944 - March 27, 1945.
BOARD HOST: Allan W. Howerton (E-mail: Allanhowerton@aol.com)