Applying for Ph.D in Public Health or Health Services without a related masters degree?

[HealthNHigherEd]

So I am interested in program planning and teaching in the field of public health in a university setting. I have my BSPH, but I am finishing up a MS.Ed. in Student Affairs Administration. I plan on getting my CHES certification and my final internship at a university women's or health center to add to my resume, but will that be enough? I'm afraid I won't stand out as I will be competing with those who have their MPH or some other related field. I just would like to get some advice or ways to approach this, Thanks!