Applying to PhD programs when you have two research interests
I'm not sure how to go about this when I have two distinctly different areas that I'm very interested in


A PhD research project is judged on many attributes, one of which is if it has a single focused reasonable, scientifically interesting and unique research question or null hypothesis that can be studied/test. 

You seem to have a problem identifying between two of your interests. This is quite common, scholars always have a number of interests and choosing one among them could be daunting and anxiety inducing, but the simple fact is that it is better to take control of the situation and decide between one of them, lest other external factors decide that for you with you having no say. 

Also, please mind that it is not just your interest that decides your research project, but a myriad of factors such as your guide's and the research group/department's own long-running interests, laboratory facilities, your long term plan (how will your PhD help you in your career), etc. Please look at the topic again against other factors you might have ignored - you will find that your two topics are not equally attractive. 

If you still can't, you could probably identify two guides and write two research proposals. The quality of each may suffer since you will divide your attention between them. But you might have postponed your decision crisis. 


  When my past professors ask me for my research interests I want to mention both of these 


Guides usually will prefer their PhD candidates to be utterly loyal to their one research project - fidelity will ensure that the project has your undivided attention. Having two interests is not wrong in any way, but might be less appealing to a Guide. You may want to downplay the other interests.