Sharon, my standard caveat before beginning: I am a hobbyist and not an expert. I will share with you what I believe to be true, but be sure to confirm all info independently.
Does the paperwork you have list any unit info? If so, you can use it to gain insight to his WWII experience. Here is a web page with info about Iwo Jima. You will find that if you scroll down to and click the "Task Organizations" link, you will be directed to a page which includes the units who took part in the battle for Iwo Jima. It includes Marine Corps, Navy, and Army units. I believe the Army units are followed by a (USA), for "Unitied States Army". If he was in the Army and took part in the Iwo Jima campaign, it was no doubt in one of these listed units.
The info Ms. Hunting provided is available in the National Archives WWII enlistment database. If it is, indeed, your father, it tells us he was in the Army. If you do not have his unit info in your papers, you can use his serial number (listed in the Archives database info) to seek his military record from NPRC. Follow this link for info on how to proceed in that regard: http://www.archives.gov/st-louis/military-personnel/index.htmlhttp://www.archives.gov/st-louis/military-personnel/index.html
Guessing from the info in your post, I believe you will also find that he qualified for the Asiatic-Pacific Campaign medal. It would signify his participation in battles in that Theater (e.g. Eastern Mandates and Iwo Jima). I believe the "two bronze service stars" which you alluded to would signify such participation, and would be affixed to the ribbon apropos to the Asiatic-Pacific Campaign medal.
This will get you started. Perhaps others can contribute additionally, expand upon this info, or make corrections if I have erred. Good luck.