Resume advise

[Rustydroid]

Hi everyone I was not sure where to post this and since there probably is a lot of adults like me pursuing college degrees I thought this would be a perfect place. So a position for a supervisor just came up. My boss is encouraging me to apply for the position. However I'm almost certain that they are going to want a resume and I've worked in the same place for over a decade so I haven't had to fill out a resume in awhile. 
I'm working towards three degrees currently but unfortunately I have no completed a single one yet. I'm currently five units away from an Electronics degree at TESU utilizing my Navy schooling and classes that I've taken in college. I need two more units in Electronics and the capstone. I'm also three classes away from an Associate's in Business at my local college.
I decided awhile back to pursue the BSBA in Accounting due to the way my job pays for classes and the TESU residency requirement. I was going to complete the electronics degree once I was done with my BSBA and had residency at TESU. The associate's in Business would just tack on once I was done with my math requirements for the BSBA. 
There is some politics being played out and I think that they are thinking about promoting a female coworker into that position. I have far more experience in the field and my boss has a say in the process and I'm sure he will root for me. 
However she has an Associate in Liberals Arts and a Bachelors in Kinisiology from a local University. I on the other hand have around 100 college credits and no degree. 
My question is what is everyone's thoughts on putting related coursework under my resume? I've been reading some online posts and it seems this more geared towards people with little work history. 
Also the classes that I've taken pertain more to the position that I'm applying for. Classes like Financial Accounting, Managerial Accounting, Business Law, Business Communications. The company that I work for has tried to become more "corporate" in the last few years and they love to use Business terminology. Years ago when I inquired about moving into that position I was told that it was more of "Business" position and since I was a technician that I didn't have the relevant training.