Both the University of Iowa, and UI Healthcare are implementing Two-Step Login with Duo Security.
However, every account used with Duo Security is an entirely separate account, with separate enrollment. If you have both a HawkID and a HealthcareID account, you will enroll each one individually. You will have the flexibility to define different two-step methods (mobile app, SMS, phone call) for each account. When you login to an application, only the methods you have defined for that account will be available for you to use. To illustrate, on your mobile smart phone, after enrolling both accounts you will see the following:
Instructions for enrolling your HawkID account are at https://its.uiowa.edu/support/article/106591
Instructions for enrolling your HealthCareID account are at http://hcis.healthcare.uiowa.edu/documents/DuoSecurityBrochure.pdf
In addition, if you choose to use your Duo Security Mobile App for two-step login for personal accounts (bank, email, facebook, etc), you may end up with many accounts listed in your Duo Mobile app, something like this: