I have always pronounced the word [実父]{じっぷ}, and it seems the dictionaries agree. (jisho.org. Also WWWJDIC, I would put a link here, but it seems the link I get on WWWJDIC is dynamic and the content can't be reproduced with a link.)
However, I just heard this word said in an anime as [実父]{じつふ}. I have not heard this pronunciation before. How common is it? I found this page with a list of pronunciation variants including じっぷ、ちち、おやじ、じつぷ with their textual usage percentages, but じつふ is not among them. (The semantic nuances are not within the scope of this question.)
This 知恵袋 thread seems to confirm [実父]{じつふ} as a possible pronunciation. But is it regional?