Image access
FYI - Access to the Cook County collections was removed in 2013, because of contract changes. The images I downloaded before that from the marriage collection were all marriage licenses, with little more information than the index.
Images for the "Illinois, Cook County Marriages, 1871-1920" collection can now be accessed by ordering the microfilm, ordering from Cook County or requesting a digital copy from the Family History Library. These options are more fully described under "Image Visibility"or requesting a digital copy from the Family History Library. These options are more fully described under "Image Visibility"
Finding the "Milling" marriage
You apparently have her maiden name and birth date and place. Have you found her in U.S. census records, before and after 1912? What do these say about when she immigrated / naturalized / first married ? Can a timeline be developed as to whether she was already married when she arrived in the U.S. ? This information may help you find her passenger list. Have you checked for her and her family in Danish records? (Not my area of expertise, but others have had success with the online records, keeping in mind that many Danish surnames were patronymic).